N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System

*Savina Nodari and Francesco Fioretti*

#### **Abstract**

The interest in n-3 polyunsaturated fatty acids (n-3 PUFAs), their favorable effects on the cardiovascular (CV) risk profile and prevention of CV events has been growing over the years, leading to their recommendation for secondary prevention in post myocardial infarction and hypertriglyceridemia. However, years later conflicting results provided by clinical trials have generated some doubts about their CV benefits, leading to a limited indication for the treatment of hypertriglyceridemia. Only recently, after the REDUCE-IT Trial results on CV events and mortality, n-3 PUFAs have recovered an indication in the international guidelines for hypertriglyceridemia in patients with Atherosclerotic Cardiovascular Disease (ASCVD) or with type 2 diabetes mellitus (T2DM) and other CV risk factors, already on statin therapy. Multiple beneficial CV effects have been highlighted, in addition to the well-known lipidlowering function, such as anti-inflammatory, anti-thrombotic and endothelial function protective properties. Three formulations of n-3 PUFAs are currently available on the market, sharing some pharmacokinetic and pharmacodynamic characteristics, but also exhibiting peculiar mechanisms. Three major clinical trials evaluated the efficacy and safety of different formulations of n-3 PUFA: JELIS, REDUCE-IT and STRENGTH, with controversial results attributable to various factors. For the future, it could be useful to perform comparative studies between different formulations and placebo, in order to clarify these doubts.

**Keywords:** n-3 PUFAs, cardiovascular diseases, cardiovascular prevention, coronary artery disease, IPE

#### **1.  The carbon chain (C) can vary greatly in length, with a range between 2 and 36 C atoms. They are divided into saturated, monounsaturated and polyunsaturated according to the number of double bonds C = C present in their molecule (respectively none, one or more than one). FA have both a systematic and common name (e.g., octadecanoic or stearic acid) [2] and are often expressed with a schematic formula (abbreviated notation): CN: p n-x,

**Figure 1.**

*Chemical structure of key saturated (A) and unsaturated (B) fatty acids. Modified from Wu H et al. [1]. DHA, docosahexaenoic acid; DPA, docosapentaenoic acid; EPA, eicosapentaenoic acid.*

where CN represents the total number of atoms of C, p the number of double bonds, x the position of the first double bond from the methyl end (n) [3].

Polyunsaturated (PUFA) n-3 (Omega 3, PUFA n-3) and n-6 (Omega 6, PUFA n-6 Fatty Acids), whose first double bond is respectively on the third and sixth atom of C (numbered by the methyl group of the carbon chain), have a particular biological and medical interest [3].

Linoleic (AL) and alpha-linolenic (ALA) acids are defined as **"**essentials," because they cannot be synthesized *de novo* in humans and must, therefore, be taken with the diet (**Table 1**). Moreover, they are considered the precursors of the n-3 and n-6 PUFA families [4].

*PUFA n-3***.** They include ALA (18,3 n-3) of plant origin and FA of animal origin (in particular seafood**—**fish oil), mainly represented by eicosapentaenoic acids (EPA; 20:5 n-3), docosahexaenoic acids (DHA; 22:6n-3) and docosapentaenoic acids (DPA, 22:5 n-3). It has been shown that ALA induces CV benefits in observational studies [5] and fish intake protects against coronary heart disease risk [6]. Moreover, a negative correlation between n-3 PUFAs and CV mortality has been reported in clinical trials and meta-analyses [7].

*PUFA n-6*. The main n-6 PUFAs are AL and arachidonic acid (AA). AL is the main n-6 PUFA derived by food and is contained in vegetable oils, nuts and seeds; AA is mainly taken from red meat, eggs, seaweed and fish oil [1]. A high intake of n-6 PUFAs, predominantly AL, would appear to be associated with a reduced risk of ischemic heart disease, ischemic stroke and CV mortality [8].

Several studies have shown the importance to maintain the balance between n-6 and n-3 PUFAs rather than the absolute quantity of each individual molecule. The centrality of this balance has been emphasized not only in the cardiology context, but

*N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

*a Data reported as mg/100 g.*

*b Content of* n *6,* n *3 FAs may slightly vary according to species, sources and analytical methods.*

*Modified from Russo GL et al. [10]. LA, Linoleic Acid; ALA, Alfa-linolenic acid; AA, Arachidonic acid; EPA, eicosapentaenoic acid; DHA, docosahexaenoic acid.*

#### **Table 1.**

*Dietary sources of principal polyunsaturated fatty acids (PUFAs)a, b.*

also in the pathogenesis of oncological, inflammatory and autoimmune diseases. The pleiotropic effects of PUFAs are summarized in **Table 2** [9].

For example, a high n-6/n-3 ratio is considered harmful to human health, while a value close to 1 is considered protective against degenerative diseases [10].

In healthy subjects taken a typical Swedish diet, a serum PUFA n-6/n-3 ratio of 4.72:1 was observed to be associated with an increase in the number of leukocytes and platelets and VEGF levels, when compared with an n-6/n-3 PUFA ratio of 2.6:1, observed in individuals following a Mediterranean diet. This dietary comparison and

#### **Antithrombotic and antiplatelet**

Decreased platelet aggregation: EPA decreased platelet aggregation and inhibited AA-induced thromboxane A2 formation

Decreased platelet adhesion:

Decreased thromboxane A2/increased thromboxane A3 levels:

#### **Anti-inflammatory**

Decreased hsCRP:

Decreased pentraxin-3: In patients with CAD treated with PCI, EPA added to statin therapy after 9 months reduced pentraxin 3 levels vs. statin alone

Decreased Lp-PLA2: In ANCHOR, IPE 4 g/day decreased Lp-PLA2 by 19.6% in patients with hsCRP >2.0 vs. placebo

Decreased NLRP3 inflammasome activation:

Decreased toll-like receptor 4: EPA reduced gene expression of toll-like receptor 4 by >50% in mice fed a high-fat diet vs. control

Decreased NFKb: EPA reduced the genetic expression of NFKb in a cell culture with THP-1 macrophages

Decreased inflammatory cytokines:

Increased anti-inflammatory cytokine IL-10:

Decreased endothelial adhesion molecules:

**Increased "resolution of inflammation": specialized pro-resolving mediators**

RvE1 was found to bind to the LTB4 receptor, BLT1, on human PMNs and attenuated LTB4-induced proinflammatory signals and PMN migration in an *in vitro* study

RvE2 was found to enhance phagocytosis of human macrophages and anti-inflammatory cytokine (IL-10) production

RvE3 was found to have potent inhibitory action on neutrophil chemotaxis both *in vitro* and *in vivo*

#### **Anti-oxidant**

Increased paraoxonase in patients with type 2 DM:

Inhibition of lipid/lipoprotein oxidation:

#### **Improved endothelial function**

EPA significantly increased NO production and reduced glucose inhibition of NO in cultured human endothelial cells

EPA significantly improved FMD by 51% in patients with elevated TG (*P* < 0.0001); EPA/AA ratio was found to be significantly associated with the change in FMD (*P* = 0.010)

EPA improved PFBF during reactive hyperemia to the level in normolipidemic controls, recovery of PFBF correlated positively with EPA levels (*P* < 0.05) and the EPA/AA ratio (*P* < 0.01)

EPA improved vascular function as measured by strain gauge plethysmography in patients with type 2 DM on statin therapy

EPA improved endothelial function in patients with CAD, LDL-C < 100 mg/dL on statin therapy, and impaired FMD

EPA with an atorvastatin metabolite improved endothelial function through increased NO in an *in vitro* study

#### **Increased cholesterol efflux**

Increasing EPA phosphatidylcholine content of reconstituted HDL-C was demonstrated to increase cholesterol efflux

EPA inhibited glucose-induced membrane cholesterol crystalline domain formation in an *in vitro* study using multilamellar vesicles

EPA and DPA inhibited oxidation of membrane cholesterol domains in an *in vitro* study utilizing multilamellar vesicles

#### **Increased adiponectin**

EPA after 3 months significantly increased adiponectin vs. placebo among obese patients with dyslipidemia (*P* < 0.01)

Change in pulse wave velocity, a measure of arterial stiffness, was negatively correlated with change in adiponectin (*P* < 0.01) and in IL-10 expression of monocytes (*P* < 0.05)

#### **Anti-arrhythmic**

EPA may reduce the risk of ventricular arrhythmia by inhibiting the fast sodium current (INa), L-type calcium inward current (ICa) and enhancing the slowly activating delayed rectifying outward potassium current (IKS), thus shortening cardiac action potential

EPA reduces cytosolic Ca2+ overload, thus reducing the risk of triggered induced arrhythmia

*Modified from Trivedi K et al. [11]. AA, arachidonic acid; apo, apolipoprotein; BLT1, leukotriene B4 receptor BLT1; Ca2+, calcium; CAD, coronary artery disease; DHA, docosahexaenoic acid; DPA, docosapentaenoic acid; DM, diabetes mellitus; EPA, eicosapentaenoic acid; FMD, flow-mediated dilation; hsCRP, high-sensitivity C-reactive protein; HDL-C, high-density lipoprotein cholesterol; ICAM, intercellular adhesion molecule; IL, interleukin; IPE, icosapent ethyl; LTB4, leukotriene B4 receptor 1; LDL-C, low-density lipoprotein cholesterol; Lp-PLA2: lipoprotein- associated phospholipase A2; MCP, monocyte chemoattractant protein; mRNA, messenger ribonucleic acid; NFKb, nuclear factor kappa-lightchain-enhancer of activated B cells; NLRP3, NLR family pyrin domain containing 3; NO, nitric oxide; PCI, percutaneous coronary intervention; PFBF, peak forearm blood flow; PON, paraoxonase; PMNs, polymorphonuclear leukocytes; REDUCE-IT, Reduction of Cardiovascular Events with Icosapent Ethyl–Intervention Trial; Rv, resolvin; sdLDL, small dense LDL; THP-1, monocyte/macrophage; TNF-α, tumor necrosis factor alpha; VLDL-C, very-lowdensity lipoprotein cholesterol; VCAM, vascular cell adhesion molecule.*

#### **Table 2.**

*Select pleiotropic effects of EPA.*

the respective clinical implications are the basis for the recognition of the importance of the Mediterranean diet in maintaining a better state of health, enough to be included in the list of Intangible Heritage of Humanity of UNESCO [11].

#### **2. Molecular mechanisms of n-3 PUFAs**

N-3 PUFAs produce multiple effects, as anti-inflammatory, anti-thrombotic properties and actions on endothelial function, in addition to the well-known lipid lowering and hypotriglyceridemic effects (**Figure 2**).

The molecular mechanisms by which n-3 PUFAs exert their pleiotropic activity are complex and not yet fully defined.

Firstly, n-3 PUFAs are embedded in the cell wall and organelles, altering the lipid environment of membranes and their fluidity. This involves n-3 PUFAs in various cellular functions, such as signal transduction and protein transport. The beneficial effects of n-3 PUFAs observed in patients with hypertriglyceridemia seem to derive from their specific actions on inflammation, platelet function and monocyte phenotypes.

In particular, the production of specialized mediators, such as E-series resolvins derived from EPA and protectins and D-series resolvins derived from DHA, can play an important role in the resolution of inflammation. The reduction of the inflammatory response by n-3 PUFAs contributes to inhibit the development of intracellular second messengers, such as diacylglycerol and ceramide. In addition, n-3 PUFAs bind and activate different nuclear receptors and transcriptional factors involved in regulating the expression of different genes. These genes participate in functions related to

#### **Figure 2.**

*Molecular pathways affected by n-3 PUFA. Taken from Mozaffarian D et al. [12]. DNA = deoxyribonucleic acid; ERK = extracellular signal-regulated kinase; mRNA = messenger ribonucleic acid; PMN = polymorphonuclear leukocyte.*

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

atherosclerosis, such as inflammation, glucose-insulin homeostasis, lipid metabolism and adipocytokine production.

Finally, the activation of the peroxisome proliferator-activated receptor-γ by n-3 PUFAs results in the reduction of the translocation of NF-κB in the nucleus, decreasing the generation of multiple inflammatory cytokines [1].

### **3. Mechanisms underlying hypolipemic effect of n-3 PUFAs**

Although the effect of n-3 PUFA-based drugs to reduce plasma triglycerides (TG) is widely recognized, their mechanism of action is not fully understood. The results of preclinical and clinical studies suggest that n-3 PUFAs reduce plasma TG concentrations by limiting their synthesis, but also by decreasing their incorporation into very low density lipoproteins (VLDLs), reducing their secretion and improving the clearance of TG by VLDLs [13, 14].

It has been proposed that n-3 PUFAs exert these effects through several mechanisms (**Figure 3**):

#### **Figure 3.**

*Proposed mechanisms of action of prescription formulations of long-chain omega-3 fatty acids. Taken from Backes J et al. [15]. ApoCIII apolipoprotein CIII, acetyl Co-a acetyl coenzyme a, DGAT diglyceride acyltransferase; FAfatty acid, LPL lipoprotein lipase,TG triglyceride, VLDL very-low-density lipoprotein.*

4.increase the expression of lipoprotein lipase (LPL), a key component of the biosynthetic pathways of TG-rich lipoproteins (TRLs), resulting in greater removal of TG by VLDLs and circulating chylomicrons.

The primary constituents of n-3 PUFA formulations, EPA and DHA, have both been shown to reduce TG. However, the two n-3 PUFAs are known to produce different effects on LDL-C and HDL-C [17]. In a meta-analysis of studies in which the effects of DHA and EPA were directly compared, DHA was associated with a greater reduction in TG, but also with a greater increase in LDL-C compared to EPA. In addition, DHA was associated with an increase in HDL-C compared to placebo, but not compared to EPA. Further studies are needed to clarify the mechanisms and significance of these differences [17].

N-3 PUFAs have also been shown to reduce circulating levels of apolipoprotein CIII (ApoCIII), believed to be involved in the progression of atherosclerosis and CV diseases (CVDs) through multiple mechanisms, such as activation and potentiation of pro-inflammatory pathways. In addition, it inhibits the receptor-mediated absorption of TRLs and their remnants, slowing their clearance and promoting the formation of small dense LDL particles from VLDLs. ApoCIII also provides a key contribution to the pathogenesis of hypertriglyceridemia, mainly due to its inhibitory action on LPL that hydrolyzes plasma TRLs, producing free FA, chylomicron remnants and intermediate density lipoproteins (IDL). Some IDL particles may undergo further LPL-mediated hydrolysis, converting to LDL.

It has been hypothesized that the different effects of DHA and EPA on the lipid profile can be explained with their different interactions with ApoCIII synthesis. DHA is believed to reduce ApoCIII synthesis by regulating some hepatic transcriptional factors, such as hepatic nuclear factor-4-alpha (HNF4A) and forkhead box-O transcription factor O1 (FOXO1). In this context, DHA promotes more hydrolysis of VLDLs, resulting in greater conversion of VLDLs into LDL, ultimately resulting in the formation of larger, less dense LDL particles. Further studies are necessary to clarify these properties.

In addition to the TG-reducing effect, n-3 PUFAs have beneficial effects on cardiometabolic risk factors, having proved to significantly reduce markers of inflammation associated with atherosclerosis and the development of CVDs.

Clinical studies showed that levels of lipoprotein-associated phospholipase A2 (Lp-PLA2) are reduced by n-3 PUFAs and icosapent ethyl (IPE) compared to placebo, and that the concentration of high-sensitivity C-reactive protein (CRP) is decreased by IPE [18, 19]. Preclinical and clinical studies have also shown that EPA and DHA have antiarrhythmic and antioxidant effects, improving endothelial function and promoting a less atherogenic lipoprotein profile when administered in combination with statin therapy [20]. Moreover, EPA and DHA reduce biomarkers of platelet activity compared to placebo, regardless of concomitant intake of aspirin and statins, and this is supposed to be associated with inhibition of platelet aggregation. Regarding this latter property, DHA is believed to possess more intensive antiplatelet activity than EPA. In addition, DHA has been shown to reduce blood pressure and heart rate, and to play a protective effect on cognitive decline.

Although most studies on the therapeutic effects of n-3 PUFAs focused on EPA and DHA, a recent study investigated the mechanism of action of DPA. DPA levels were independently associated with a reduced risk of developing acute myocardial infarction (AMI) and coronary artery disease (CAD), while reduced circulating levels of

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

DPA were shown to be associated with the development of lipid-rich plaques and peripheral arterial disease (PAD).

EPA, DHA and DPA counteract platelet aggregation in a dose-dependent manner. However, DPA seemed to be the most intensive inhibitor of platelet activity, compared with EPA and DHA. As DHA and EPA, also DPA can reduce the expression of pro-inflammatory genes.

The mechanisms underlying the reduction of TG by long-chain n-3 PUFAs differ from those of other lipid-lowering drugs, such as statins. Therefore, if administered in combination, different lipid-lowering drugs could potentially have complementary beneficial effects on the lipid profile [13]. As proof of this, incremental reductions in TG levels were observed when n-3 PUFAs are administered with statins [21].

#### **3.1 n-3 PUFAs and atheromatous plaques**

The inverse relationship found between the intima-media thickness of the carotid artery and the treatment with n-3 PUFAs suggested their endothelium protective activity and anti-atherosclerosis effect. There is specific evidence that this result is achieved through a reduction in inflammation and increased plaque stability.

The relationship between the vulnerability of atheromatous plaque and the serum n-3/n-6 PUFA ratio was evaluated in a study that enrolled patients undergoing percutaneous coronary angioplasty [22]. The EPA/AA ratio was examined at the time of the patient's admission. An angioscopy examination of the culprit coronary lesion evaluated the color tone of the plaque (white 0; light yellow 1; yellow 2; intense yellow 3) and the possible presence of a thrombus. Patients with stable angina (n = 38) were divided into 2 groups based on a reduced (<0.37; n = 19) or elevated (≥0.37; n = 19) EPA/AA ratio. In the group with reduced EPA/AA, the maximum yellow tone of the plaques was significantly higher than in patients with stable angina and high EPA/AA ratio. Moreover, the number of non-culprit yellow plaques with a thrombus tended to be higher, without reaching statistical significance. Multivariate analysis revealed an association between a lower serum EPA levels with lower EPA/AA ratio and the finding of more vulnerable grade 3 yellow plaques.

In another trial, 49 thin-cap non-culprit atheromatous plaques (TCFA) were evaluated in 30 patients with untreated dyslipidemia [23]. Patients were randomized to EPA (1.8 g/day) + rosuvastatin (n = 15, 23 TCFA) or rosuvastatin alone (n = 15, 26 TCFA). Percutaneous interventions and a 9-month follow-up OCT were performed to assess morphological changes in TCFA. The EPA/AA ratio and pentraxin-3 (PTX3) levels were also evaluated.

Despite LDL-C levels during follow-up were comparable in the two groups, subjects treated with EPA + statin had a higher EPA/AA ratio and lower PTX3 levels than those receiving the statin alone. The OCT also showed that in the EPA + statin group there was a greater increase in the thickness of the fibrotic cap, a more evident reduction of the lipid arch and its length, as well as a lower macrophage accumulation. Such evidence suggested that concomitant use of EPA and rosuvastatin contributes to the stabilization of a vulnerable plaque compared with the use of statin alone and, presumably, through inhibition of arterial wall inflammation.

The recent randomized, double-blind controlled clinical trial EVAPORATE [24] evaluated the volume of atheromatous plaque, using multidetector CT (MDCT), after treatment with 4 g/day of IPE in combination with diet and statin therapy versus statin alone. The study enrolled 80 patients with coronary atherosclerosis documented by MDCT (one or more stenosis with narrowing >20%), already on statin therapy and with elevated TG levels (median value in both groups of 259.1 78.1 mg/dL). MDCTs follow-up were performed after 9 and 18 months. The primary endpoint was low attenuation volume changes (LAP volume) at 18 months. In the IPE group the LAP plaque volume was reduced by 17%, while in the control group it was more than doubled (+109%; P = 0.0061). Significant differences were also observed in the progression index of other plaques, such as fibrous and fibro-adipose plaques, whose volumes decreased in the IPE group and progressed in the placebo group (P < 0.01).

#### **4. Different pharmacological formulations (OM3EE, OM3CA, IPE, EPA/DPA/DHA EE)**

#### **4.1 General aspects**

PUFA n-3 formulations are recommended, in combination with diet, for the reduction of serum TG in adults with hypertriglyceridemia.

Mainly three formulations of PUFA n-3 are currently available [13]:

#### **4.2 Bioavailability**

The absorption of DHA and EPA has been shown to vary between formulations. The OM3CA formulation has a bioavailability (area under the "plasma concentration-time" curve from zero to the last measured concentration value [AUC(0-t)]) of fourfold greater for both EPA and DHA during low-fat consumption than observed with OM3EE [12]. Absorption of OM3EE and IPE requires pancreatic lipase-mediated hydrolysis. Since pancreatic lipase levels depend on both the amount and type of lipids ingested, the absorption of OM3EE is thought to depend strongly on the fat content of meals. In contrast, n-3 PUFAs in the free FA form, contained in OM3CA formulations, are not dependent on pancreatic lipase hydrolysis. Therefore, the bioavailability of EPA and DHA present in this formulation is less dependent on meal fat content than in OM3EE formulations. In one study (n = 54), conducted under

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

low-fat intake conditions, 59% of subjects treated with OM3CA maintained an AUC(0-t) for EPA and DHA ≥50% compared to the AUC(0-t) observed under high-fat intake. In contrast, this finding was present in only 6% of OM3EE-treated subjects. This observation could be useful from a therapeutic point of view, as current guidelines recommend a very low fat diet in patients with severe hypertriglyceridemia [25].

#### **4.3 Efficacy**

All n-3 PUFA formulations, administered at a dose of 4 g/day, have been shown to significantly reduce TG, VLDL-C, non-C-HDL, and ApoB levels in hypertriglyceridemic and high CV risk patients [13]. Higher doses of n-3 PUFAs and higher baseline triglyceridemia levels are associated with greater percentage of reductions in TG [26]. This was also observed in the MARINE trial, in which different dosages of highly purified EPA ethyl ester (Vazkepa) were compared (**Figure 4**). This effect appears to be independent from the severity of hypertriglyceridemia.

In the JELIS study, the use of a formulation of highly purified EPA ethyl ester (Epadel) was shown to reduce CV events when combined with statin and a reduction in atheromatous plaque thickness. It has also demonstrated a good safety and tolerability profile.

In REDUCE-IT trial, on the other hand, 4 g/day of EPA ethyl ester was shown to result in favorable effects in terms of reducing ischemic events and CV mortality.

In contrast, in the STRENGTH trial, which used the OM3CA (EPA + DHA) formulation, a neutral effect in terms of CV outcome (MACE) was observed, thus not supporting the hypothesis of using n-3 PUFAs for CV event risk reduction.

DHA-containing formulations (OM3CA and OM3EE) may cause an increase in C-LDL levels, especially in patients with severe hypertriglyceridemia (TG >500 mg/dL). However, this is not associated with increased levels of non-HDL C or ApoB, which seems to be a better predictor of CV risk than C-LDL values [13]. This is particularly true for patients with hypertriglyceridemia, who often have low LDL-C levels [25].

Non-DHA-containing formulations (EPA and IPE) appear not to cause an increase in C-LDL levels [12], as shown in the MARINE [27] and ANCHOR [28] clinical trials, which studied efficacy and safety of IPE.

These different effects of EPA versus DHA on C-LDL levels can be attributed to one or more mechanisms:

#### **Figure 4.**

*Change in lipid levels, baseline to week 12 (intent-to-treat population). Percentage of change from baseline to study end of placebo-corrected lipid levels in patients with very high TG levels receiving AMR101 4 g/day or AMR101 2 g/day. Modified from Bays HE et al. [17]. APO-B = apolipoprotein B; cHDL = high-density lipoprotein cholesterol; cLDL = low-density lipoprotein cholesterol; Lp-PLA2 = lipoprotein associated phospholipase A2; n-cHDL = non-high-density lipoprotein cholesterol; NS = not significant; Tot-Chol = total cholesterol; Tryg = triglyceride; cVLDL, very-low-density lipoprotein cholesterol; VLDL–TG, very-low-density lipoprotein–triglycerides.*

Interestingly, in patients with triglyceridemia >200 mg/dL but <500 mg/dL, no increase in LDL-C was observed with any of the formulations. This is probably because in the various clinical trials on n-3 PUFAs, such patients had lower baseline serum TG levels and were already on statin therapy.

It was also observed that, unlike IPE, DHA-containing formulations increased HDL-C levels. However, the clinical relevance of increasing HDL-C through pharmacological agents has not been clarified yet.

In contrast, to date, the effect of any n-3 PUFA formulation on pancreatitis has not been determined [13].

EPA and DHA are also believed to act in different or conflicting ways at the cell membrane level. Specifically, the insertion of EPA and DHA occurs in distinct regions of the lipid membrane bilayer as a consequence of the different lengths of the hydrocarbons involved. Their insertion causes conformational changes that result in increased membrane fluidity and promotion of cholesterol domains. Among the 2 n-3 PUFAs, EPA has a more stable and extended structure, which contributes to membrane stability as well as inhibition of lipid oxidation and formation of new cholesterol domains [29]. Their main effects are summarized in **Figure 5**.

#### **4.4 Safety and tolerability**

Commercially available n-3 PUFA formulations are generally well tolerated, with similar rates of treatment discontinuation between treatment and placebo groups [13]. In clinical trials, gastro-intestinal events were the main adverse effects with DHA-containing formulations, while arthralgia was the main adverse event reported with EPA [12].

In the REDUCE-IT trial, it was observed a higher incidence of atrial fibrillation and peripheral edema in the treatment group versus placebo group (5.3% vs. 3.9% and

*N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

**Figure 5.** *Molecular membrane interactions of omega-3 fatty acids. Taken from Mason RP et al. [28].*

6.5% vs. 5.0%, respectively). The possible pathogenetic mechanisms could be related to their effects on myocyte membrane ion channels. Previous observational and randomized studies have examined the potential antiarrhythmic effects of n-3 PUFAs, leading to conflicting results [30, 31]. However, in the REDUCE-IT trial, the increased incidence of atrial fibrillation in the EPA-treated group was not associated with a higher incidence of heart failure or stroke. Therefore, further studies are required to clarify these aspects.

In both JELIS and REDUCE-IT, modest increases in bleeding episodes were observed in the EPA-treated group compared with controls. Bleeding rates were lower in JELIS (1.1% in EPA vs. 0.6% in control group) than in REDUCE-IT (2.7% with EPA vs. 2.1% with placebo). In JELIS study antiplatelet therapy, at baseline, was present in 13% and 14% in treatment and placebo groups, respectively, compared with 79.7% and 79.1%, respectively, in the REDUCE-IT (26). Although no serious bleeding events were observed in REDUCE-IT or in other clinical trials with n-3 PUFAs, even in those who were on aspirin or warfarin therapy and in those undergone surgery or percutaneous interventions, the potential interaction between EPA and antithrombotic drugs warrants further investigation.

It is not known whether patients with allergies to fish and/or shellfish are at increased risk of allergic reactions to n-3 PUFAs. Therefore, these formulations should be used with caution in patients with known hypersensitivity to fish and/or shellfish [13].

#### **4.5 Differences from n-3 PUFA-based dietary supplements**

PUFA n-3 dietary supplements are widely used and they are among the most popular dietary supplements worldwide. However, they are not subject to the strict regulations required for prescription drugs. As a result, the EPA and DHA content of dietary supplements can be variable or too low [13].

Physicians often tend to erroneously consider n-3 PUFA dietary supplements to be adequate and reliable. However, a recent analysis of individual fish oil supplements has shown that they contain an inadequate dose of EPA and DHA, on average equivalent to only 68% of that required. The same analysis found that most supplements exceed the recommended levels of oxidation markers. The oxidative process undergone by n-3 PUFAs results in a gradual reduction in their concentration, leading to reduced efficacy. One study showed that a median intake of 11 servings of fish oil dietary supplements per day was needed to obtain a dose of 3.4 g/day of n-3 PUFAs. The same study showed that dietary supplements often contain other fats and cholesterol, and that their content varies widely among different products. Such variability can be confusing for patients, as well as for physicians, resulting in a drug dosage potentially inadequate to effectively reduce serum TGs in patients with hypertriglyceridemia [29]. Based on this evidence, we conclude that, to date, the benefits of n-3 PUFA-based nutraceuticals are uncertain and their use controversial [13].

#### **5. Controlled clinical trials of different formulations of n-3 PUFAs. Efficacy on lipid profile and outcomes**

The efficacy on lipid profile and outcomes of controlled clinical trials are summarized in **Figure 6** and **Table 3**, respectively. **GISSI-Prevention trial (1999)**. This multicenter [32] "open-label" study evaluated 11,324 patients with recent (<3 months) AMI randomized equally into four treatment groups: group 1, n-3 PUFAs (850–882 mg EPA and DHA as ethyl esters in EPA/DHA 1,2 ratio); group 2, vitamin E (300 mg, in 1 cps of synthetic α-tocopherol); group 3, n-3 PUFAs + vitamin E; control group 4 (no supplement). Combined primary efficacy endpoint represented by cumulative rate of all-cause mortality, nonfatal AMI, and nonfatal stroke; and cumulative rate of death from CV causes, nonfatal AMI, and nonfatal stroke.

*N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

#### **Figure 6.**

*TG reduction observed with varying doses of omega-3 carboxylic acids, omega-3 ethyl esters, and icosapent ethyl in (a) patients with severe hypertriglyceridemia (TG* ≥ *500 mg/dL) and (b) statin-treated patients with high baseline TG levels (TG level* ≥ *200 mg/dL and < 500 mg/dL). Taken from Backes J et al. [15]. OM3CA = percentage change from baseline expressed as least-squares geometric mean; OM3EE = percentage change from baseline expressed as geometric mean; IPE = percentage change from baseline expressed as median. † Placebo used = olive oil; ‡ placebo used = vegetable oil; § placebo used = mineral oil; <sup>ǁ</sup> placebo used = corn oil; ¶ Placebo not specified. IPE icosapent ethyl, OM3CA omega-3 carboxylic acids, OM3EE omega-3 ethyl esters,TG triglyceride.*

Secondary analyses were performed for each component of the primary endpoints and for major causes of death.

Treatment with n-3 PUFAs, but not vitamin E, significantly reduced the primary endpoint (RR reduction of 10% (95% CI 1–18) with two-way analysis of variance and 15% (2–26) with four-way analysis). Benefits were attributed to reduction in risk of death (14% (3–24) with two-way, 20% (6–33) four-way) and CV death (17% (3–29) two-way, 30% (13–44) four-way). No significant change in C values (total, HDL, LDL) nor fibrinogen was observed in all groups.

In comparison with the control group, the slight reduction in triglyceridemia was shown more frequently in patients treated with PUFA n-3. The effects of combined treatment were similar to those observed in treatment with n-3 PUFAs alone, for both the primary endpoint (14% (1–26)) and fatal events (20% (5–33)).

These results demonstrate the statistically significant clinical benefits of dietary supplementation with n-3 PUFAs, where vitamin E supplementation demonstrated no benefit.

**JELIS (Japan EPA Lipid Intervention Study; 2007)**. Randomized "open label" trial with blinded endpoint analysis [33] evaluated the long-term prevention effects of EPA of major coronary events in patients with hypercholesterolemia.

Over a 3-year period, 18,645 patients (60% women; mean age 61 years) with coronary artery disease (established angina pectoris, coronary interventions, previous AMI; n = 3664) or free of coronary artery disease (n = 14,981), with baseline total C value >250 mg/dL (corresponding to C-LDL >170 mg/dL) were enrolled. First-line therapy for all patients consisted of pravastatin 10 mg or simvastatin 5 mg once daily (20 mg pravastatin and 10 mg simvastatin in severe hypercholesterolemia). Primary endpoints were major coronary events: sudden cardiac death, fatal and nonfatal AMI, and nonfatal events such as development of unstable angina, CABG, angioplasty, and/ or coronary stenting. Patients were randomized to treatment with EPA (EPA+ statin) or statin alone (controls).

After a mean follow-up of 4.6 years, the primary endpoint had occurred in 262 patients (2.8%) in the EPA group and 324 patients (3.5%) in the control group, with a

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

**Table 3.**

*Reviewed outcomes trials of n-3*

 *PUFAs.* relative 19% reduction in major coronary events (p = 0.011). The 25% reduction in C-LDL in both groups after treatment was not found to be a significant factor in reducing the risk of events. The risk of unstable angina and nonfatal coronary events was reduced by 19% in the EPA group, while sudden cardiac death and death from coronary causes were overlapping in the 2 groups.

In patients with coronary artery disease (secondary prevention), EPA reduced major coronary events by 19% compared with controls (8.7% vs. 10.7%; p = 0.048). In patients free of coronary artery disease, EPA did not significantly reduce major coronary events (18%; 1.4% vs. 1.7% of controls; p = 0.132). The study results suggested that EPA was a promising treatment for primary and secondary prevention of major coronary events, especially nonfatal coronary events (**Figure 7**).

A sub-analysis of JELIS in 2012, showing 38% (p = 0.007) reduction in coronary events in patients who did not reach target values of C-LDL and non-C-HDL, concluded that EPA supplementation was also more effective in patients who did not reach target values of cholesterolemia.

**REDUCE-IT (2019)**. Multicenter, randomized, placebo-controlled, double-blind study [34] enrolled and followed, on average for 4.9 years, 8179 patients diagnosed with CV disease (70.7%; secondary prevention) or with diabetes mellitus and other risk factors on statin therapy. Patients had to have triglyceridemia between 135 and 499 mg/dL and C-LDL between 41 and 100 mg/dL at baseline.

The aim of the study was to evaluate the potential benefits of EPA ethyl ester on CV outcomes in patients with elevated triglyceridemia levels. Patients were randomized to receive 2000 mg of the EPA ethyl ester twice daily (with a total dose of 4 g) or placebo (mineral oil).

The primary composite endpoint was the association of CV death, nonfatal AMI, nonfatal stroke, coronary revascularization, or unstable angina. Key secondary endpoints were the association of CV death, nonfatal AMI, and nonfatal stroke.

The primary endpoint occurred in 17.2% of patients in the EPA group compared with 22% of controls (HR 0.75; 95% CI, 0.68–0.83; p < 0.001). Secondary endpoints were observed in 11.2% of EPA and 14.8% of placebo patients, respectively (HR 0.74; 95% CI, 0.65–0.83; p < 0.001). The rate of ischemic events was significantly lower in the EPA group than in the placebo group, as was the CV mortality rate (4.3% vs. 5.2%; HR 0.80; 95% CI, 0.66–0.98; p = 0.03).

Regarding the safety profile of EPA, it was observed that hospitalization for atrial fibrillation or flutter occurred in a significant proportion of EPA-treated patients

#### **Figure 7.**

*Kaplan-Meier estimates of incidence of coronary events in the total study population (panel 1), the primary prevention arm (panel 2), and the secondary prevention arm (panel 3). Modified from Yokoyama et al. [33]. HR = Hazard ratio.*

(3.1% vs. 2.1%; p = 0.004). Serious bleeding events occurred in 2.7% of EPA patients and 2.1% of controls (p = 0.06).

The study shows that in patients with elevated triglyceridemia, even with statin therapy, the risk of ischemic events and CV death is further reduced by EPA supplementation (**Figure 8**).

**STRENGTH (2020)**. Multicenter, randomized, double-blind study [35], which evaluated the effects of carboxyl formulation (CA) of EPA and DHA on CV outcomes in adult patients on statin therapy for at least 4 weeks and with elevated CV risk, defined by the presence of:

A total of 13,078 patients were enrolled in 675 community and teaching hospitals and 22 states in North America, Europe, South America, Asia, Australia, New Zealand, and South Africa. All included patients had high TRI values (between 180 and 499 mg/dL) and low C-HDL values (<42 mg/dL in men, <47 mg/dL in women). More than 50% of the enrolled patients met the criteria for secondary CV prevention. Patients were randomized to receive 4 grams/day of CA n-3 PUFAs (n = 6539) or corn oil placebo (n = 6539), in combination with usual medical therapy.

The primary composite efficacy endpoint was an association of CV death, nonfatal AMI, nonfatal stroke, coronary revascularization, and hospitalization for unstable angina. Secondary endpoints included (1) the association of CV death, nonfatal IMA, nonfatal stroke, coronary revascularization, and hospitalization for unstable angina in

#### **Figure 8.**

*Cumulative incidence of cardiovascular events in REDUCE-IT trial. Modified from Bhatt et al. [34]. HR = Hazard ratio.*

*N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

#### **Figure 9.**

*Time to first incidence of any component of the primary composite end point (1) and time to Core major adverse cardiovascular events (2). Modified from Nicholls SJ et al. [35]. 1, the primary composite end point consisted of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, coronary revascularization and hospitalization for unstable angina. 2, Core major adverse cardiovascular events included cardiovascular death, nonfatal myocardial infarction and nonfatal stroke.*

patients with pre-existing CVD at baseline, (2) the association of CV death, nonfatal IMA, and nonfatal stroke in the whole cohort of patients and in patients with preexisting CVD at baseline, (3) the association of cardiac death, nonfatal AMI, coronary revascularization, and hospitalization for unstable angina in the entire cohort of patients and in those with pre-existing CVD at baseline, (4) CV death in the entire cohort of patients and in those with pre-existing CVD at baseline, and (5) all-cause mortality in all patients and in those with pre-existing CVD at baseline.

When 1384 patients developed a primary endpoint event (compared with 1600 expected), the trial was stopped early on the basis of a biased analysis of the data, which showed a low likelihood of clinical benefit of n-3 PUFA CA compared with placebo. Study population baseline characteristics were as follows: mean age 62.5 + 9.0 years; 35% women; 70% with diabetes; median C-LDL 75.0 mg/dL; median triglyceride levels 240 mg/dL; median HDL-C levels 36 mg/dL; and median hsPCR 2.1 mg/L. Out of 12,633 patients (96.6%) who completed the trial, the primary end point occurred in 785 (12.0%) treated with n-3 PUFAs compared with 795 (12.2%) treated with corn oil (HR, 0.99 [95% CI, 0.90–1.09]; P = 0.84). There was, in addition, a high rate of gastrointestinal adverse events in the treatment group (24.7% vs. 14.7%).

Therefore, the results of this study do not support the use of PUFA n-3 formulations for improving clinical outcome in patients at high CV risk and on statin therapy (**Figure 9**).

#### **5.1 REDUCE-IT and STRENGTH trials: Why conflicting results?**

Several hypotheses have been developed to interpret the reasons that led REDUCE-IT and STRENGTH (two high-quality studies that employed full doses of n-3 PUFAs), to deeply conflicting results [36].

1.One possible explanation theorizes that in the REDUCE-IT study, EPA did not reduce the risk of CV events but, rather, its comparator (mineral oil) increased them. An increase in C-LDL, apoB, and hsPCR associated with mineral oil seems to support this interpretation. However, a U.S. FDA review of the REDUCE-IT

results concluded that this hypothesis could explain only part of the highlighted difference between EPA and mineral oil.

To resolve the discrepancies between STRENGTH and REDUCE-IT, regulatory agencies such as the FDA could authorize a post-marketing clinical trial comparing high-dose EPA vs. corn oil in patients at high risk of developing CV events.

#### **6. Real word data about n-3 PUFAs**

**TG-REAL (2020).** Longitudinal, retrospective cohort study that used 3 administrative databases from 3 Italian local health authorities [37]. It included 158,042 individuals with at least one serum TG assay between January 1, 2010 and December 31, 2015. Individuals with normal TG values (<150 mg/dL; n = 142,289) were compared with patients with high values (150–500 mg/dL; n = 15,558) and those with very high values (>500 mg/dL; n = 195).

The outcomes were atherosclerotic CV events (ASCVD) and all-cause mortality. Overall, the incidences of ASCVD and all-cause mortality were 7.2 and 17.1 per 1000 individual-years, respectively. After multivariate correction for potential confounding factors, in individuals with high and very high TG values, there was a significant increased risk of all-cause mortality (HR = 1.49 (95 percent CI 1.36–1.63), p < 0.001, and HR = 3.08 (95 percent CI 1.46–6.50), p < 0.01, respectively), and of ASCVD (HR = 1.61 (95 percent CI 1.43–1.82), p < 0.001, and HR = 2.30 (95 percent CI 1.02–5.18), p < 0.05, respectively).

The TG-REAL study captured real-world data related to a large cohort of patients with low-to-moderate CV risk, demonstrating how moderate to severely elevated TG values are associated with a significant increased risk of ASCVD and all cause death.

#### **7. Final considerations**

Following the results of the REDUCE-IT trial, the regulatory agencies FDA and EMA have given their approval for the use of n-3 PUFAs in patients at high CV risk in

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

order to reduce atherosclerotic-based events. The recommendations for the use of n-3 PUFAs in the more recent European and US guidelines are shown in **Table 4** [9].

An Update is expected from the European Scientific Societies. In fact, in the 2019 European Society of Cardiology (ESC) guidelines, the recommendation for the use of n-3 PUFAs in high-risk patients with hypertriglyceridemia is still class IIa, despite the positive results that have recently emerged from clinical trials.

*a Bold text highlights aspects of expanded label indication that notably differ from language in updated guidelines and REDUCE-IT entry criteria.*

*Modified from Trivedi K et al. [11]. ADA, American Diabetes Association; AHA, American Heart Association; CV, cardiovascular; EAS, European Atherosclerosis Society; EPA, eicosapentaenoic acid; ESC, European Society of Cardiology; FDA, Food and Drug Administration; LDL-C, low-density lipoprotein cholesterol; MI, myocardial infarction; NLA, National Lipid Association; REDUCE-IT, Reduction of Cardiovascular Events with Icosapent Ethyl– Intervention Trial; TG, triglyceride.*

#### **Table 4.**

*Statements from medical societies and the US FDA regarding IPE (pure EPA) post-REDUCE-IT.*

Currently, the strategy for the management and prevention of CV diseases follows the so-called "ABCDEF" scheme.

In that strategy:

Based on current evidence, it is believed that under "E," along with exercise, the intake of EPA and IPE, rather than fish oil dietary supplements, should also be considered as a "new entry."

#### *N-3 Polyunsaturated Fatty Acids and Their Role on Cardiovascular System DOI: http://dx.doi.org/10.5772/intechopen.110145*

It is also important to note that previous studies on n-3 PUFAs, in which there was a goal of lowering TG levels, have not obtained concordant results regarding their efficacy in reducing CV events. These conflicting results seem attributable to several factors, including frequent use of inappropriate drug dosages, use of different formulations, and/or inadequate selection of the target population. Therefore, it is of great relevance to find answers to the outstanding questions and to overcome the biases highlighted in past clinical trials. Such doubts or questions could only be clarified by performing comparison studies between different available formulations, such as those used in the REDUCE-IT and STRENGTH clinical trials, in order to fully understand the real differences in terms of efficacy and safety of these drugs.

Finally, it is important to point out that IPE therapy has been shown to be closely related to a reduction in the residual risk of total ischemic events in patients with ASCVD or with type II diabetes mellitus and other CV risk factors, already on statin therapy. These evidences would therefore support a preferential indication for the use of IPE over currently marketed formulations.

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Author details**

Savina Nodari\* and Francesco Fioretti Cardiology Unit, Department of Medical and Surgical Specialties, Radiological Sciences and Public Health, University and Spedali Civili Hospital of Brescia, Brescia, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 4**


**Proposition 4.**

For item (a), the non-negativity of *F*(*ρS*|Π, *U*) follows from inequality (16) in Proposition 2. The upper bound is evident in view of inequality (32).

For item (b), let *c* ∈ [0, 1], *ρS* and *σS* be two states with *ρS* = Φ*S*(*ρS*), *σS* = Φ*S*(*σS*). Straightforward manipulation yields

$$\begin{aligned} &cF(\rho\_S|\Pi,\mathsf{II}) + (1-c)F(\sigma\_S|\Pi,\mathsf{II}) - F(c\rho\_S + (1-c)\sigma\_S|\Pi,\mathsf{II}) \\ &= c(1-c)\left(\mathsf{tr}((\rho\_S - \sigma\_S)^2) - \mathsf{tr}((\rho\_S' - \sigma\_S')^2)\right) \\ &\ge 0. \end{aligned}$$

The last inequality follows from

$$
\lambda (\rho\_S' - \sigma\_S') \nrightarrow \lambda (\rho\_S - \sigma\_S).
$$

We see that, on the one hand, *D*(*ρS*|Π, *U*) and *F*(*ρS*|Π, *U*) share some similar properties, and, on the other hand, they have different advantages and disadvantages. This is reminiscent of the comparison between the conventional variance and Fisher information.

#### **4. Influence on Environment Caused by System**

The interaction between the system and the environment is mutual. While we are focusing on the decoherence of the system caused by the environment, it may also be useful to investigate the influence on the environment caused by the system. In a formal fashion, this may also be interpreted as the decoherence of the environment caused by the system. Due to the asymmetry of the system–environment interaction, there are subtle differences between the influence on the environment caused by the system and that on the system caused by the environment.

From Equation (20), we obtain the final environment state

$$\rho\_E' = \text{tr}\_S \rho\_{SE}' = \sum\_{i=1}^d \text{tr}(\Pi\_i \rho\_S) \mathcal{U}\_{E\_i} \rho\_E \mathcal{U}\_{E\_i}^\dagger = \sum\_{i=1}^d p\_i \mathcal{U}\_{E\_i} \rho\_E \mathcal{U}\_{E\_i}^\dagger$$

after the system–environment interaction. Here *pi* = tr(*ρS*Π*i*) = *i*|*ρS*|*i*-. We denote the above operation as

$$\Phi\_E(\rho\_E) = \rho\_E' = \sum\_{i=1}^d p\_i \mathcal{U}\_{E\_i} \rho\_E \mathcal{U}\_{E\_i}^\dagger$$

which is a random unitary channel with Kraus operators √*piUEi* . Moreover, noting that *ρE* = *ρE*1 ⊗ *ρE*2 ⊗···⊗ *ρEd* , we have

$$J(\rho\_E, \Phi\_E) = 1 + \text{tr}\left(\sqrt{\rho\_E} \Phi\_E^\dagger(\sqrt{\rho\_E})\right) = 1 + \sum\_{i=1}^d p\_i \text{tr}(\sqrt{\rho\_E} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho\_E} \mathcal{U}\_{E\_i})$$

$$= 1 + \sum\_{i=1}^d p\_i \text{tr}(\sqrt{\rho\_{E\_i}} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho\_{E\_i}} \mathcal{U}\_{E\_i})\tag{33}$$

and

$$J(\rho\_{E'}', \Phi\_E) = 1 + \text{tr}\left(\sqrt{\rho\_E'} \Phi\_E^\dagger(\sqrt{\rho\_E'})\right) = 1 + \sum\_{i=1}^d p\_i \text{tr}\left(\sqrt{\rho\_E'} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho\_E'} \mathcal{U}\_{E\_i}\right)$$

The final state of the *i*-th sub-environment reads

$$\rho'\_{E\_i} = \text{tr}\_{E\_i} \rho'\_E = \text{tr}\_{E\_i} \left( \sum\_{i=1}^d p\_i \mathcal{U}\_{E\_i} \rho\_E \mathcal{U}\_{E\_i}^\dagger \right) \\ = p\_i \mathcal{U}\_{E\_i} \rho\_{E\_i} \mathcal{U}\_{E\_i}^\dagger + (1 - p\_i) \rho\_{E\_i}.$$

where the notation tr*E*2*i* denotes the partial trace over all sub-environments except for *Ei*. We denote the corresponding operation as the channel

$$\Phi\_{E\_i}(\rho\_{E\_i}) = \rho\_{E\_i}' = p\_i \mathcal{U}\_{E\_i} \rho\_{E\_i} \mathcal{U}\_{E\_i}^\dagger + (1 - p\_i)\rho\_{E\_i}$$

which is also a random unitary channel. The classicality of the environment can be evaluated as

$$J(\rho\_{\mathbb{E}\_i}, \Phi\_{\mathbb{E}\_i}) = 1 + \text{tr}\left(\sqrt{\rho\_{\mathbb{E}\_i}} \Phi\_{\mathbb{E}\_i}^\dagger(\sqrt{\rho\_{\mathbb{E}\_i}})\right) = 2 - p\_i + p\_i \text{tr}(\sqrt{\rho\_{\mathbb{E}\_i}} \mathcal{U}\_{\mathbb{E}\_i}^\dagger \sqrt{\rho\_{\mathbb{E}\_i}} \mathcal{U}\_{\mathbb{E}\_i}) \tag{34}$$

,

and

$$J(\rho'\_{E\_i\prime}, \Phi\_{E\_i}) = 1 + \text{tr}(\sqrt{\rho'\_{E\_i}} \Phi\_{E\_i}^\dagger(\sqrt{\rho'\_{E\_i}})) = 2 - p\_i + p\_i \text{tr}(\sqrt{\rho'\_{E\_i}} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho'\_{E\_i}} \mathcal{U}\_{E\_i}).$$

Comparing Equations (33) and (34), we get

$$(2 - J(\rho\_{E'} \Phi\_E) = \sum\_{i=1}^d \left(2 - J(\rho\_{E\_i'} \Phi\_{E\_i})\right)\_{i=1}$$

or equivalently,

$$I(\rho\_{E'}, \Phi\_E) = \sum\_{i=1}^d I(\rho\_{E\_{i'}}, \Phi\_{E\_i})\_{i'}$$

which shows a kind of additivity property, as intuitively expected since the initial environment is in a product state *ρE* = *ρE*1 ⊗ *ρE*2 ⊗···⊗ *ρEd* .

In terms of the classicality *J*(*ρE*, Φ*E*) of the environment, we define the influence on the total environment caused by the system as

$$D(\rho\_E|\mathbf{U}, \Pi) = f(\rho\_{E'}^\prime \Phi\_E) - f(\rho\_{E'} \Phi\_E) \tag{35}$$

and the influence on the *i*-th sub-environment caused by the system as

$$D(\rho\_{E\_i}|\mathcal{U}, \Pi) = f(\rho\_{E\_{i'}}', \Phi\_{E\_i}) - f(\rho\_{E\_{i'}}, \Phi\_{E\_i}), \tag{36}$$

.

respectively. Compared with Equation (27), we have deliberately swapped the place of *U* and Π to indicate the difference of the reference channels. The influence on the environment caused by the system can be explicitly evaluated as

$$D(\rho\_E|\mathcal{U}, \Pi) = \sum\_{i=1}^d p\_i \text{tr}\left(\sqrt{\rho\_E'} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho\_E'} \mathcal{U}\_{E\_i} - \sqrt{\rho\_E} \mathcal{U}\_{E\_i}^\dagger \sqrt{\rho\_E} \mathcal{U}\_{E\_i}\right).$$

Similarly,

$$D(\rho\_{E\_i}|\mathcal{U}, \Pi) = p\_i \text{tr}\left(\sqrt{\rho\_{E\_i}^{\prime}} \mathcal{U}\_{E\_i}^{\dagger} \sqrt{\rho\_{E\_i}^{\prime}} \mathcal{U}\_{E\_i} - \sqrt{\rho\_{E\_i}} \mathcal{U}\_{E\_i}^{\dagger} \sqrt{\rho\_{E\_i}} \mathcal{U}\_{E\_i}\right)^{\dagger}$$

If we use the alternative quantifier of classicality *C*(*ρ*, K), then the classicality of the initial and final environment states with respect to the reduced environment channel can be evaluated as

$$\begin{aligned} \mathbb{C}(\rho\_E, \Phi\_E) &= 1 - \text{tr}(\rho\_E^2) + \sum\_{i=1}^d p\_i^2 (2 - p\_i d\_i) + d - 2 \\ \mathbb{C}(\rho\_{E'}^{'}, \Phi\_E) &= 1 - \text{tr}(\rho\_E^{'2}) + \sum\_{i=1}^d p\_i^2 (2 - p\_i d\_i) + d - 2. \end{aligned}$$

where *di* is the dimension of the *i*-th sub-environment. In terms of the classicality of the environment *C*(*ρE*, Φ*E*), we have an alternative measure of influence on the total environment caused by the system as

$$F(\rho\_E|\mathbf{U}, \Pi) = \mathbb{C}(\rho\_{E'}'\Phi\_E) - \mathbb{C}(\rho\_{E'}\Phi\_E).$$

and the influence on the *i*-th environment caused by the system as

$$F(\rho\_{E\_i}|\mathbf{U}, \Pi) = \mathbb{C}(\rho\_{E\_{i'}}' \Phi\_{E\_i}) - \mathbb{C}(\rho\_{E\_{i'}} \Phi\_{E\_i})\_{\prime}$$

respectively. It turns out that

$$\begin{aligned} F(\rho\_E|\mathbf{U}, \Pi) &= \text{tr}(\rho\_E^2) - \text{tr}(\rho\_E'^2) \\ F(\rho\_{E\_i}|\mathbf{U}, \Pi) &= \text{tr}(\rho\_{E\_i}^2) - \text{tr}(\rho\_{E\_i}'^2) .\end{aligned}$$

These quantities of influence on the environment (caused by the system) may be compared with the quantifiers of decoherence of the system (caused by the environment), and they should be correlated due to the system-environment coupling.

#### **5. Illustrating Decoherence in Interferometry**

with

We illustrate the effectiveness of the quantifiers proposed in the preceding section with a two-path interferometer, as depicted in Figure 2. The system Hilbert space of interest here is effectively a qubit space with the two paths labeled as Π1 = |0-0| and Π2 = |1-1|. Let the initial system state (the path degree part of the physical state) be

$$\rho\_S = \frac{1}{2} \left( \mathbf{1} + \sum\_{i=1}^3 r\_j \sigma\_{\bar{\jmath}} \right) = \frac{1}{2} \begin{pmatrix} 1 + r\_3 & r\_1 - ir\_2 \\ r\_1 + ir\_2 & 1 - r\_3 \end{pmatrix} \tag{37}$$

with the Bloch vector *r* = (*r*1,*r*2,*r*3) ∈ R3 satisfying |*r*| = *r*21 + *r*22 + *r*23 ≤ 1 and *σj* being the Pauli spin matrices. The eigenvalues of *ρS* are (1 ± |*r*|)/2. It can be directly evaluated that

$$
\sqrt{\rho\_S} = \frac{1}{2\sqrt{\gamma}} \begin{pmatrix} \gamma + r\_3 & r\_1 - ir\_2 \\ r\_1 + ir\_2 & \gamma - r\_3 \end{pmatrix}
$$

$$
\gamma = 1 + \sqrt{1 - |r|^2}.\tag{38}
$$

$$\begin{array}{c|c} \Pi\_{\mathcal{U}} = \Pi\_1 \otimes U\_{E\_1} + \Pi\_2 \otimes U\_{E\_2} \\ \rho\_S = \begin{array}{c} \text{Path } \Pi\_1 = |0\rangle(0| \\ \hline \end{array} \\ \rho\_{E\_1} = \begin{array}{c} \text{Path } \Pi\_1 = |0\rangle(0| \\ \hline \end{array} \\ \rho\_{E\_2} = |1\rangle(1| \\ \hline \end{array} \\ \rho\_{E\_2} = |1\rangle(1| \\ \hline \end{array} \\ \rho\_E' = \text{tr}\_S \rho\_{SE}'$$

**Figure 2.** Schematic illustration of decoherence induced by the array of path detectors *U* = {*UEi* : *i* = 1, 2} (serving as the environment of the system state *ρS*) attached to the collection of path Π = {Π*i* : *i* = 1, 2}. Each path Π*i* is probed by a detector *UEi* . The initial system state is *ρS*, while the initial array of detector state is *ρE* = *ρE*1 ⊗ *ρE*2 . The combined initial state is *ρSE* = *ρS* ⊗ *ρE*. The system–detector coupling is via the combined unitary operator Π*U* = ∑2*i*=1 Π*i* ⊗ *UEi* , and the final combined system is *ρSE* = Π*U ρSE*Π†*U* with final system state *ρS* = tr*ρSE*. The decoherence of *ρS* (with respect to Π) induced by the path detectors are quantified by *D*(*ρS*|Π, *U*) = *J*(*ρS*, Π) − *J*(*ρS*, Π) and *F*(*ρS*|Π, *U*) = *C*(*ρS*, Π) − *C*(*ρS*, Π), which are the increasing amount of classicality of the system state caused by the path detectors.

For a two-path interferometer with a detector attached to each path, let *ρEi* be the initial detector state attached to path *i*; the system and detector evolve under the controlled-*U* operation

$$
\Pi\_{\mathcal{U}} = \Pi\_1 \otimes \mathcal{U}\_{E\_1} + \Pi\_2 \otimes \mathcal{U}\_{E\_2}.\tag{39}
$$

 From an information-theoretic point of view, this controlled-*U* operation correlates the quantum system and the detector and leads to the combined final state

$$\begin{split} \rho'\_{SE} &= \Pi\_{\mathcal{U}} (\rho\_S \otimes \rho\_E) \Pi\_{\mathcal{U}}^{\dagger} \\ &= (\Pi\_1 \rho\_S \Pi\_1) \otimes (\mathcal{U}\_{E\_1} \rho\_E \mathcal{U}\_{E\_1}^{\dagger}) + (\Pi\_1 \rho\_S \Pi\_2) \otimes (\mathcal{U}\_{E\_1} \rho\_E \mathcal{U}\_{E\_2}^{\dagger}) \\ &+ (\Pi\_2 \rho\_S \Pi\_1) \otimes (\mathcal{U}\_{E\_2} \rho\_E \mathcal{U}\_{E\_1}^{\dagger}) + (\Pi\_2 \rho\_S \Pi\_2) \otimes (\mathcal{U}\_{E\_2} \rho\_E \mathcal{U}\_{E\_2}^{\dagger}). \end{split} \tag{40}$$

The final system state can be obtained by taking the partial trace over the detector as

$$\begin{split} \rho'\_{S} &= \text{tr}\_{E}\rho'\_{SE} \\ &= \Pi\_{1}\rho\_{S}\Pi\_{1} + \Pi\_{1}\rho\_{S}\Pi\_{2}\text{tr}(\mathcal{U}\_{E\_{1}}\rho\_{E}\mathcal{U}\_{E\_{2}}^{\dagger}) + \Pi\_{2}\rho\_{S}\Pi\_{1}\text{tr}(\mathcal{U}\_{E\_{2}}\rho\_{E}\mathcal{U}\_{E\_{1}}^{\dagger}) + \Pi\_{2}\rho\_{S}\Pi\_{2} \\ &= \frac{1}{2}\begin{pmatrix} 1 + r\_{3} & (r\_{1} - ir\_{2})\mathcal{V}^{\*} \\ (r\_{1} + ir\_{2})\mathcal{V} & 1 - r\_{3} \end{pmatrix} .\end{split}$$

with

$$\mathcal{V} = \text{tr}(\mathcal{U}\_{E\_2}\rho\_E \mathcal{U}\_{E\_1}^\dagger) = \text{tr}(\mathcal{U}\_{E\_2}\rho\_{E\_2}) \cdot \text{tr}(\rho\_{E\_1}\mathcal{U}\_{E\_1}^\dagger)$$

being a complex number. By the Cauchy–Schwarz inequality, we have

$$\begin{split} \left| \left| \mathcal{V} \right|^{2} = \left| \text{tr} \left( (\mathcal{U}\_{E\_{2}} \sqrt{\rho\_{E}}) (\mathcal{U}\_{E\_{1}} \sqrt{\rho\_{E}})^{\dagger} \right) \right|^{2} \\ \leq & \text{tr} \left( (\mathcal{U}\_{E\_{2}} \sqrt{\rho\_{E}}) (\mathcal{U}\_{E\_{2}} \sqrt{\rho\_{E}})^{\dagger} \right) \cdot \text{tr} \left( (\mathcal{U}\_{E\_{1}} \sqrt{\rho\_{E}}) (\mathcal{U}\_{E\_{1}} \sqrt{\rho\_{E}})^{\dagger} \right) \right| \\ = & 1. \end{split}$$

The eigenvalues of *ρS* = Φ*S*(*ρS*) are

$$\lambda\_1(\rho\_S') = \frac{1}{2} \left( 1 + \sqrt{r\_3^2 + (r\_1^2 + r\_2^2)|\mathcal{V}|^2} \right) \tag{41}$$

$$
\lambda\_2(\rho\_S') = \frac{1}{2} \left( 1 - \sqrt{r\_3^2 + (r\_1^2 + r\_2^2)|\mathcal{V}|^2} \right). \tag{42}
$$

Consequently, we see that

$$
\lambda\left(\rho\_S'\right) \prec \lambda\left(\rho\_S\right),
$$

as it should be by Proposition 2.

> Noting that

$$
\sqrt{\rho\_S'} = \frac{1}{2\sqrt{\gamma'}} \begin{pmatrix} \gamma' + r\_3 & (r\_1 - ir\_2)\mathcal{V}^\* \\ (r\_1 + ir\_2)\mathcal{V} & \gamma' - r\_3 \end{pmatrix} \tag{49}
$$

$$
\gamma' = \pm \sqrt{\frac{1}{1 + (\gamma' + r\_1)(111^2 - r\_2^2)}} \tag{40}
$$

where

$$\gamma' = 1 + \sqrt{1 - (r\_1^2 + r\_2^2)|\mathcal{V}|^2 - r\_{3'}^2} \tag{43}$$

we obtain

$$\begin{split} D(\rho\_S|\Pi, \Pi) &= J(\rho\_S', \Pi) - J(\rho\_S, \Pi) \\ &= \left(\frac{\gamma' + r\_3}{2\sqrt{\gamma'}}\right)^2 + \left(\frac{\gamma' - r\_3}{2\sqrt{\gamma'}}\right)^2 - \left(\frac{\gamma + r\_3}{2\sqrt{\gamma}}\right)^2 - \left(\frac{\gamma - r\_3}{2\sqrt{\gamma}}\right)^2 \\ &= \frac{1}{2}(\gamma' - \gamma)\left(1 - \frac{r\_3^2}{\gamma'\gamma}\right). \end{split} \tag{44}$$

Since *γ* ≥ *γ*, *γ* ≥ 1 ≥ *r*3, we see readily that the above quantity is non-negative. Moreover, because *γ* is a decreasing function of |V|2, from Equation (44) we see that *D*(*ρS*|Π, *U*) is a decreasing function of |V|2.

Similarly, we can evaluate

$$\begin{aligned} \mathcal{C}(\rho'\_{S'}\Pi) &= 1 - \frac{1}{4} \left( (1+r\_3)^2 + (r\_1^2 + r\_2^2)|\mathcal{V}|^2 + (1-r\_3)^2 + (r\_1^2 + r\_2^2)|\mathcal{V}|^2 \right) \\ &+ \frac{1}{4} \left( (1+r\_3)^2 + (1-r\_3)^2 \right) \\ &= 1 - \frac{1}{2} (r\_1^2 + r\_2^2)|\mathcal{V}|^2 \end{aligned}$$

from which we obtain

$$F(\rho\_{\mathcal{S}}|\Pi, \mathcal{U}) = \mathbb{C}(\rho\_{\mathcal{S}}', \Pi) - \mathbb{C}(\rho\_{\mathcal{S}}, \Pi) = \frac{1}{2}(r\_1^2 + r\_2^2)(1 - |\mathcal{V}|^2),\tag{45}$$

which is also apparently a decreasing function of |V|.

It can be easily verified that both the decoherence quantifiers *D*(*ρS*|Π, *U*) and *F*(*ρS*|Π, *U*) are decreasing functions of |V|, and achieve the minimal value 0 when |V| = 1, which corresponds to the situation when the detector does not obtain the path information. In this case, coherence is preserved, and there is no decoherence. This is consistent with our intuition since decoherence can be regarded as the washing out of interference, while *D*(*ρS*|Π, *U*) and *F*(*ρS*|Π, *U*) can be regarded as measures of path information leakage to the detectors (classical path information). The detectors, from which we can obtain the path information of the quantum system, would inevitably reduce the interference ability of the quantum system.

The quantity V = tr(*UE*2*ρEU*† *E*1) arises naturally in at least two other contexts:

 (a) If we take *UE*1 = **1** and *UE*2 = *U*, then we come to the setup of Englert [34], in which |V| is the fringe visibility in the complementarity relation

$$|\mathcal{V}|^2 + \mathcal{D}^2 \le 1,$$

with D = 1 2 tr|*UρEU*† − *ρE*| being the quantitative measure of distinguishability. In this context, V is also called the interference function.

(b) If we define the generalized variance of measuring any operator *X* in state *σ* as

$$V(\sigma, X) = \text{tr}\left(\sigma (X - \text{tr}(\sigma X)) (X - \text{tr}(\sigma X))^\dagger\right),$$

and consider the unitary operator *U*† *E*1*UE*2 = *U*† *E*1⊗ *UE*2 , then we have

$$\begin{split} \mathcal{V}(\rho\_{E'} \mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2}) &= \text{tr}\{\rho\_E(\mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2} - \text{tr}(\rho\_E \mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2}))(\mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2} - \text{tr}(\rho\_E \mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2}))^\dagger\} \\ &= 1 - |\text{tr}(\mathcal{U}\_{E\_2} \rho\_E \mathcal{U}\_{E\_1}^\dagger)|^2 \\ &= 1 - |\mathcal{V}|^2 \end{split}$$

which is a kind of measure of path detecting capability. The above relation immediately leads to

$$V(\rho\_{E'} \| \boldsymbol{I}\_{E\_1}^\dagger \boldsymbol{\mathcal{U}}\_{E\_2}) + |\mathcal{V}|^2 = 1,$$

which is apparently a complementary relation between the path information and fringe visibility. Furthermore, combined with Equation (45), we have

$$F(\rho\_S|\Pi, \mathcal{U}) = \frac{1}{2} (r\_1^2 + r\_2^2) V(\rho\_{E\_1} \mathcal{U}\_{E\_1}^\dagger \mathcal{U}\_{E\_2}) \,\prime$$

which relates the decoherence directly with the path-detecting information. This is consistent with our intuitive understanding of decoherence as the information leakage to the detectors (environment).

Now we make some comparison of our quantifiers of decoherence with existing ones. Since, in general, decoherence is also regarded as the establishment of correlations between the system and environment, it is expected that decoherence should be related to correlations, as quantified by the mutual information between the system and the environment. For simplicity, we consider the setup described by Figure 2 and assume that the initial system state and environment state are both pure. In this case, the final system–environment state *ρSE* is pure since the coupling Π*U* is unitary. Consequently, the mutual information of the final system–environment state is

$$I(\rho\_{SE}') = S(\rho\_S') + S(\rho\_E') - S(\rho\_{SE}') = 2S(\rho\_S') = 2\left(-\lambda\_1(\rho\_S')\ln\lambda\_1(\rho\_S') - \lambda\_2(\rho\_S')\ln\lambda\_2(\rho\_S')\right),$$

where *λj*(*ρ S*) are determined by Equations (41) and (42), and *S*(*σ*) = −tr *σ*ln *σ* is the von Neumann entropy of the state *σ*. Since the initial system state *ρS* defined by Equation (37) is pure, we have *r*2 1 + *r*2 2 + *r*2 3 = 1. Therefore by Equations (41), (42) and (45), we have

$$\begin{aligned} \lambda\_1(\rho\_S') &= \frac{1}{2} \left( 1 + \sqrt{1 - (r\_1^2 + r\_2^2)(1 - |\mathcal{V}|^2)} \right) = \frac{1}{2} \left( 1 + \sqrt{1 - 2F(\rho\_S|\Pi, l\mathcal{U})} \right), \\\lambda\_2(\rho\_S') &= \frac{1}{2} \left( 1 - \sqrt{1 - (r\_1^2 + r\_2^2)(1 - |\mathcal{V}|^2)} \right) = \frac{1}{2} \left( 1 - \sqrt{1 - 2F(\rho\_S|\Pi, l\mathcal{U})} \right). \end{aligned}$$

Now the mutual information can be expressed as

$$I(\rho\_{SE}') = 2H\left(\frac{1}{2}\left(1 + \sqrt{1 - 2F(\rho\_S|\Pi, \mathcal{U})}\right)\right),$$

where *H*(*p*) = −*p*ln*p* − (1 − *p*)ln(1 − *p*) is the binary Shannon entropy function, 0 ≤ *p* ≤ 1. From the above equation, we see that the mutual information is monotonically related to the decoherence: when decoherence increases, the mutual information increases, which is consistent with the intuition that larger decoherence corresponds to larger amount of correlations established between the system and the environment (larger information leakage to the environment). Although the above result is proved for initial pure states and *F*(*ρS*|Π, *U*), the general cases concerning mixed initial states and the decoherence quantifier *D*(*ρS*|Π, *U*) are similar, but the calculations are more complicated. It will be also interesting to make a more comprehensive comparative studies between various quantities related to decoherence and correlations.

### **6. Summary**

In order to quantify decoherence induced by environment, we reviewed two quantifiers of classicality in a general setup of state–channel interaction by exploiting the Jordan symmetric product and a modified notion of variance. These quantifiers may be of independent interest in addressing the classical–quantum interplay. We also elucidated some simple yet useful features of the decoherence channel (Hadamard channel).

Employing the above quantifiers of classicality, we introduced two quantifiers of decoherence induced by environment in the combined "system + environment" setup. These quantifiers have some nice properties and can be used to summarize the decoherence strength of an open system. Connections with complementarity were discussed. The results were illustrated via a two-path interferometer.

A natural approach to quantifying decoherence is via correlations between the system and the environment. There are various quantifiers for correlations such as the quantum mutual information, entanglement, quantum discord, measurement-induced disturbance, measurement-induced nonlocality, classical correlations, etc. In particular, decoherence is quantified from a decorrelating perspective in Refs. [106,107]. However, correlations are generally hard to evaluate. Our present approaches differ from the conventional approach to decoherence via correlations such as quantum mutual information. Our quantifiers of decoherence are relatively easier to calculate and have intimate relations with the Wigner–Yanase skew information, uncertainty, and the resource theory of coherence. This indicates certain operational significance of the quantities. However, it remains to further study the operational meaning of these quantifiers of decoherence and to investigate their implications for foundational issues and experimental practices.

For open quantum systems, apart from decoherence, another prominent characteristic is quantum Markovianity/non-Markovianity [108–116]. Although the classical Markovianity is uniquely defined and well understood, there is not a single universally accepted definition of quantum Markovianity. A host of quantum Markovianity-related concepts coexist, such as GKS–Lindblad master equations, distinguishability, divisibility, no-information backflow, monotonic decreasing in correlations, etc. However, just like decoherence is related to the decaying of off-diagonal entries of the density matrix, a general common feature of the various Markovianities is related to information loss and memoryless effects. This indicates that there are intimate relations between decoherence and Markovianity. We remark that the feature of decoherence as information monotonically flowing into the environment is deeply related to the Markovian approximation. In non-Markovian dynamics, in contrast to decoherence, recoherence may occur. The interplay and relations between decoherence and quantum Markovianity/non-Markovianity are worth further investigations.

**Author Contributions:** All authors contributed equally to the work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Key R&D Program of China, Grant No. 2020YFA0712700; the Fundamental Research Funds for the Central Universities, Grant No. FRF-TP-19-012A3; and the National Natural Science Foundation of China, Grant Nos. 11875317 and 61833010.

**Data Availability Statement:** Not appliable.

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


*4.6. Small RNA Library Construction and Sequencing*

RNA was extracted from spot and non-spot sepal using the modified Trizol method [6], and 4 small RNA libraries from sepal spot and non-spot samples with 2 biological replicates were constructed and sequenced by SBQ500 sequencing method (BGI, Wuhan, China). Then the low-quality, 5 primer contaminants, without 3 primers and insert tags, and sequences fewer than 18 nucleotides (nt) were filtered out to obtain clean reads from raw data reads. The final clean reads of the 4 libraries were mapped to *Phalaenopsis* genome and other smallRNA databases using Bowtie2 [41]. All the remaining clean sequences were annotated into different classes to remove rRNA, scRNA, snoRNA, snRNA, and tRNA using miRBase, siRNA, piRNA, snoRNA database with Bowtie2 [42] and Rfam database with cmsearch [43]. The novel miRNAs were predicted by Mireap software (https://sourceforge.net/ projects/mireap/).


**Abstract**

Until fairly recently, treatment options for advanced melanoma have been relatively limited. Fortunately, the last decade has seen dramatic improvements in response rates and duration of overall survival after the introduction of checkpoint inhibitors and targeted therapies against mutations in the B-isoform of Raf (B-Raf) in metastatic or inoperable melanoma. This book chapter will discuss the role of wild type B-Raf in the cell, the changes induced by mutations in this protein, and current FDA approvals for targeted therapies against B-Raf, both as a monotherapy and in combination with MEK inhibitors. We will also summarize mechanisms of resistance against these targeted therapies as well as novel therapeutic regimens proposed to bypass resistance.

**Keywords:** melanoma, metastasis, B-Raf, MEK, targeted therapy, adjuvant


**About the Editors**

**Raffaella Boggia** is an Associate Professor of Food Chemistry at the Department of Pharmacy of the University of Genoa (IT). She graduated with honors in Pharmaceutical Chemistry and Technology (University of Genoa) and in Pharmacy (University of Rome "La Sapienza"). She holds a Ph.D. in Pharmaceutical Sciences. During her post-doctoral studies, she spent periods at the Laboratory of Molecular Biophysics (Oxford University, UK) and at the Laboratory of Drug Design of Tecnofarmaci SCpA (Pomezia-Rome, Italy). Her research has focused on the formulation of nutraceutical ingredients by eco-sustainable techniques, starting from agro-industrial by-products and waste; untargeted spectroscopic fingerprints to assess food authenticity; applied chemometrics; and molecular modeling. She is the author of over 130 original publications and has participated in national and European research projects, including as a P.I.

**Paola Zunin** is an Associate Professor of Food Chemistry at the Department of Pharmacy of the University of Genoa (IT). In 1981, she graduated in Medicinal Chemistry and Pharmaceutical Technologies at the University of Genoa, and in 1982, she also graduated in Pharmacy at the same university. She has almost 40 years of experience in the field of food chemistry. Her research interests have been mainly focused on lipids in foods, with emphasis on the chemical composition of virgin olive oils and other vegetable oils, on the development of analytical methods for the assessment of their quality and authenticity, on cholesterol and phytosterol oxidation in food and dietetic products, and on the characterization of food from specific geographical areas by applying multivariate statistical methods to the results obtained by classical and innovative analytical methods. Her latest research activities are focused on the application of green extraction methods for the extraction of health-promoting molecules from agri-food wastes and on the application of innovative production technologies for the quality improvement of different foodstuffs and for the production of functional foods.

**Federica Turrini** is a Researcher at the Department of Pharmacy of the University of Genoa. Her research interests are in the fields of eco-compatible extractive technologies that have a low environmental impact and adhere to the principles of green chemistry and green extraction; application of environmentally friendly technologies assisted with ultrasounds and microwaves for the treatment of different food matrices and agri-food production waste; valorization of waste from different food processing chains for the further formulation of new potential nutraceutical and/or cosmeceutical ingredients; chemical-bromatological characterization and assessment of the authenticity of different food matrices by untargeted spectroscopic analytical technologies coupled with chemometric techniques and targeted chromatographic characterization; and formulation of new enriched and/or functional food and food dietary supplements through innovative technological treatments. In these fields of study, she is the author of scientific publications in national and international journals, and she has participated in national and EU research projects.


*5.6. Plant Materials and Ambient Temperature Treatment*

*O. fragrans* plants, cultivar "Yanhonggui", were potted and grown in the Zhejiang Agriculture and Forestry University Osmanthus Resource Nursery. The flower buds at different stages were collected between 9.00–10.00 a.m. every day, including S0 (the outer bud scales unfurled and the inner bud scales still furled); S1 (the bud became globularshaped and the inside bracts covering the inflorescence was visible); S2 (the inflorescence burst through bracts and the florets closely crowded); S3 (the florets are bud-shaped and the pedicels elongate); S4 (initial flowering stage); S5 (full flowering stage). The flower bud phenotype of *O. fragrans* at different stages are shown in Figure S1. In addition, the plants in S0 stage with similar size were selected and treated with different temperatures (19 ◦C and 23 ◦C) in a growth chamber. When treated at 19 ◦C for 2 days and 5 days, the flower buds reached S1 and S2 stages, respectively, while flower buds still remained in S1 stage when treated at 23 ◦C for 2 days and 5 days. The phenotype of flower buds in 19 ◦C and 23 ◦C are shown in Figure S2. The relative humidity was about 70% and the photoperiod was a 12 h light/12 h dark regime with illumination of 10,000 lux. Each treatment included three independent biological replications. Samples of each stage were collected and stored at −80 ◦C before total RNA extraction.


**5. Conclusions**

In conclusion, RDE enhances cell activity by directly scavenging ROS and strengthening the cellular antioxidant system, as well as by repairing tight junction proteins and inducing their expression.

**Author Contributions:** Conceptualization, C.Y. and R.Y.; Data analysis, R.Y., S.L., Q.H., H.Z. and Q.J.; Financial funding, C.Y.; Methodology, F.L., S.L., J.W. and R.Y.; Supervision, C.Y. and K.O; Writing, R.Y., C.Y. and K.O.

**Funding:** This project was funded by the Natural Sciences and Engineering Research Council (NSERC) Engage grant (C. Yang, EGP<PHONE_NUMBER>) and the University of Manitoba Start-Up Grant (C. Yang, 46561). Runqiang Yang was a Visiting Scholar at the Department of Animal Science in the University of Manitoba and supported by the Chinese Scholarship Council (CSC).

**Acknowledgments:** The authors are grateful to Red Dog Enterprises Ltd. for providing red-osier dogwood extracts.

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


*3.5. Heterogeneity of Data*

The type and frequency of data gathered varied greatly among the studies reviewed. In some papers, only one figure with one retinal section was o ffered as evidence for PR degeneration, while other papers showed extensive quantitation of their data. To document potential sources of variability in the data, we indicate the method by which the degree of degeneration was determined, either by measuring ONL thickness or by count of nuclei in the ONL, typically the number of rows of nuclei spanning the ONL but sometimes a total count of ONL nuclei in a fixed area of a retinal micrograph. In some instances, when data was quantified in spider plots or bar graphs, mean values obtained from the central retina were used in estimating the PR loss. We normalized the data among studies by recording the percent degeneration as determined by dividing the mutant values by the corresponding values from age-matched controls as reported in each publication.

### *3.6. Comparison of Progressive PR Cell Loss*

To compare progressive PR cell loss among models, we fit normalized data from each article to an exponential decay that includes a delay, or o ffset [36]. Ranges of either age or photoreceptor numbers, if reported, were averaged. Fitting was performed in Excel Visual Basic using a piecewise equation that modeled the delay with a straight line at 100% and the remaining points with a monoexponential decay to 0%. Two adjustable parameters, the delay and the decay rate constant, were optimized. We calculated the age at which PR cell numbers reached 50% of control values (D50) as a measure of progression. Roughly one third of the datasets contained only a single point within the exponential regime, which was insu fficient to calculate D50. In these cases, D50 was calculated at the extremes of zero delay and infinite rate, and the mean of these values was used as a D50 estimate.

### *3.7. Generation of Primary Data Using Fundus Imaging and OCT Scans*

Fundus photographs of EMR mutants were taken in unanesthetized mice treated with 1% cyclopentolate to dilate or enlarge the pupil with an in vivo bright field retinal imaging microscope equipped with image-guided OCT capabilities (Micron III; Phoenix Laboratories, Inc., Pleasanton, CA, USA) as previously described [20]. This system allows for the visualization of the location of the OCT scan using the real-time Micron III bright-field image. A superimposed line placed directly on the image over the retinal feature being examined delivers precise cross-sectional information, allowing for the assessment of changes in layer thickness and morphological alterations.

Fundus photodocumentation for TVRM mutants and C57BL/6J control mice was performed using a Micron III or IV retinal camera (Phoenix Laboratories, Inc., Pleasanton, CA, USA) as described [37], except that 1% cyclopentolate or 1% atropine was used as a dilating agent, and in some cases, mice were anesthetized with isoflurane. OCT imaging to assess retinal layer thickness in *Nmnat1tvrm113*, *Ctnna1Tvrm5*, and C57BL/6J control mice was performed using a Bioptigen ultrahigh-resolution (UHR) Envisu R2210 spectral domain OCT (SDOCT) imaging system for volume scanning as described [37,38] with ketamine/xylazine (1.6 mL ketamine (100 mg/mL), 1.6 mL xylazine (20 mg/mL), and 6.8 mL sodium chloride (0.9% *w*/*v*)) as an anesthetic. A representative B-scan through the optic nerve head was derived from the OCT volume dataset. *Rpgrip1nmf247* and *Alms1Gt(XH152)Byg* were assessed on the same OCT system by obtaining a linear B-scan with the following parameters: length, 1.9 mm; width, 1.9 mm; angle, 0 degrees; horizontal o ffset, 0 mm; vertical o ffset, 0 mm; A-scans/B-scan, 1000 lines; B-scans, 1 line; frames/B-scan, 20 frames; and inactive A-scans/B-scan, 80 lines. Linear scans were registered and averaged in the InVivoVue program to merge the 20 frames into a single image.


**5. Conclusions**

This study has shown the strategic interest of referring to climate and crop modeling for the prediction of the impacts of future climate change on the rainfed durum wheat yield in the High eastern plain of Algeria. For the baseline period 1981–2010, the climate model ICHEC\_KNMI used in this study has proved its reliability in simulating temperatures and net solar radiation with good precision. However, precipitations are simulated with less certainty, given the high variability of precipitation in Algeria, which made the simulation very complicated. The AquaCrop crop model was used to assess the impacts of future climate change on grain yields, length of the growth cycle, and the water productivity of the durum wheat cultivar, Mexicali, in 2035–2064, under RCP 4.5 and RCP 8.5. This study showed that the effect of the increase in CO2 concentrationsin the atmosphere made it possible to avoid the drop yields of the rainfed Mexicali cultivar. This decline in grain yield could be induced by the negative effects: of the drop in precipitation and net solar radiation and by the increased air temperatures projected over the growing season of this cultivar in 2035–2064, under RCP 4.5 or RCP 8.5. Moreover, this study proved that the increase in temperature expected in 2035–2064 under the above scenarios, causes a shortening of the duration of the growth cycle of the Mexicali cultivar. However, an increase in yields and water productivity of this cultivar are projected by this future horizon, thanks to the fertilizing effect of the enrichment of the atmosphere with CO2. This study has made it possible to plan a strategy for adapting rainfed durum wheat to rising temperatures by applying early sowing in October, which avoids the loss of yield during the wheat growth cycle very sensitive stage, of grain filling in spring. However, further research is needed, using climate projections from an ensemble of climate models instead of a single model, to reduce the observed uncertainties in the precipitation simulation. It is necessary to evaluate, under RCPs scenarios, with other crop models, the effect of supplemental irrigation and fertilization on the adaptation of this Mexicali cultivar and other durum wheat cultivars to future climate change. Thus, the association of climate and crop modeling proves to be a relevant tool that meets the needs of farmers in terms of choice of farming practices and cultivars, in order to reduce the negative impacts of climate change on crops yields, as it enables decision-makers in the agricultural sector to plan sustainable and effective policies to help farmers to face the projected climate change and avoid crop yield losses, thereby maintaining food security in Algeria.

**Author Contributions:** T.K. collected, corrected, analyzed, simulated crop data with AquaCrop, interpreted the crop and climate data and wrote the initial draft of the paper. D.S. provided some data and supervised and corrected the paper, she also, reanalyzed and reinterpreted some data and contributed in the improvement of the manuscript contain and quality. A.M. read and contributed in improvement the English editing of the paper. All authors have read and agreed to the published version of the manuscript.

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

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to restriction imposed by the National office of meteorology in Algeria.

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