**1. Introduction**

The treatment of atopic dermatitis (AD) can be challenging for dermatologists and other healthcare professionals. Conventional treatments consisting of emollients and topical corticosteroids are often insufficient for severe and/or refractory AD. Other therapies include systemic corticosteroids, photochemotherapy using psoralen and ultraviolet-A light, and cyclosporine. However, all of these approaches have potentially serious side effects and relative contraindications, especially in children. Over the past two decades, occlusive therapy has been advocated as a safe and effective treatment modality for individuals with acute erythrodermic AD and those with severe and/or refractory AD. (Nicol 1987; Goodyear et al. 1991; Bridgman 1995; Devillers and Oranje 2005)

Occlusive therapy usually involves the application of emollients, antiseptics, or topical corticosteroids under either wet wrap dressings (WWD) or dry wrap dressings (DWD). This consists of moistened open-weave cotton tubular bandages (eg. Tubifast, Tubigauz) in WWD occlusion, versus dry gauze, plastic wraps, or hydrocolloid dressings (eg. Duoderm) in DWD occlusion. (Nicol 1987; Goodyear et al. 1991; Bridgman 1995)

More recently, however, occlusion alone using a hydrogel patch has been utilized. The theory is that a major component in the pathophysiology of AD is barrier dysfunction. In fact, many current therapies target this barrier defect (i.e., pseudoceramide moisturizers and skin barrier emulsions). As such, an ideal repair mechanism would completely eliminate microbe and allergen penetration and transepidermal water loss in AD, both of which lead to xerosis, hypersensitivity, pruritus, and inflammation. The hydrogel patch, therefore, offers an innovative approach to *complete* barrier repair. (Park et al. 2011)

Regardless of the treatment approach, occlusive therapy offers many advantageous such as a cooling effect on inflamed skin, increased penetration of topical agents, enhanced skin hydration, and a barrier to external antigens and trauma (i.e. scratching). Reported disadvantages include the cumbersome and time-consuming nature of the application process, risk of allergic reaction to the occlusive material itself, and possible increased risk of infectious complications such as folliculitis, furunculosis, or cellulitis. An additional concern is that occlusion may cause skin maceration if used incorrectly, or can paradoxically

promote skin dryness if too little topicals are applied. (Nicol 1987; Goodyear et al. 1991; Bridgman 1995; Krakowski et al. 2008)

Occlusion alone of both normal and lesional eczematous skin can result in increased density of cutaneous microbial flora. (Aly et al. 1978; Rajka et al. 1981) Moreover, there is a positive association between *Staphylococcus aureus* (*S. aureus*) colonization and disease severity. (Williams 2000) These findings suggest that occlusion, by increasing the density of *S. aureus*, might push already colonized eczematous skin into the realm of clinical infection. In addition, innate production of cutaneous anti-microbial peptides, such as sphingosine and -defensin, is depressed in patients with AD such that eczematous skin possesses decreased natural resistance to bacterial invasion (Arikawa et al. 2002; Ong et al. 2002) Thus, evidence of clinically apparent skin infection may be a contraindication to occlusive therapy, as it may exacerbate the infection. (Aly et al. 1978) However, the possibility that *S. aureus* colonization may complicate occlusive therapy has not been adequately addressed to date.

Another concern is that the use of topical corticosteroids under occlusion may relate to an increased potential for absorption and greater incidences of possible adverse effects. Most attention has been focused on the risk of skin atrophy and striae, hypothalamic-pituitaryadrenal (HPA) axis suppression, as well as growth impairment in children.

Ultimately, this chapter aims to examine current evidence on the safety and efficacy of occlusive therapy in the treatment of AD.

#### **2. Methods**

Studies on the use of occlusive therapy for the treatment of atopic dermatitis were identified in PubMed and Embase Medline databases from January 1966 to April 2011, using the key terms "occlusion," "occlusive dressings", "occlusive therapy," "wet wrap," "wet dressings," "dry wrap," "dry dressings," "atopic dermatitis," "dermatitis," and "eczema." Key terms were also searched in combination. Reference lists of relevant publications were manually searched for additional relevant studies. The search was limited to original studies and review articles published in English or with English abstracts, in humans. Studies of small size and those that did not use a controlled or randomized study design were included due to the dearth of published literature on this topic. Publications meeting these criteria were then reviewed for study design, population, disease severity or type, study size, efficacy, and safety. The topical agent used, dilution, and type and period of occlusive therapy were also noted, when such information was made available in the publication. In addition, response to therapy was seen as improvement in disease severity or symptoms from baseline, improvement in SCORing Atopic Dermatitis (SCORAD), and/or improvement in Eczema Area and Severity Index (EASI) score, depending on what information was provided. Of note, SCORAD is composite score of eczema severity based on the surface area involved, intensity of symptoms, and subjective symptoms such as sleep disturbance and pruritus. EASI is a 12-point scoring system of disease severity assessing erythema, induration, lichenification, pruritus, and excoriation. Finally, conclusions were drawn from the results of these studies bearing in mind standard clinical practice.

#### **3.  Fourteen studies used WWD, 5 of which were randomized controlled trials. All WWD

270 Atopic Dermatitis – Disease Etiology and Clinical Management

promote skin dryness if too little topicals are applied. (Nicol 1987; Goodyear et al. 1991;

Occlusion alone of both normal and lesional eczematous skin can result in increased density of cutaneous microbial flora. (Aly et al. 1978; Rajka et al. 1981) Moreover, there is a positive association between *Staphylococcus aureus* (*S. aureus*) colonization and disease severity. (Williams 2000) These findings suggest that occlusion, by increasing the density of *S. aureus*, might push already colonized eczematous skin into the realm of clinical infection. In addition, innate production of cutaneous anti-microbial peptides, such as sphingosine and -defensin, is depressed in patients with AD such that eczematous skin possesses decreased natural resistance to bacterial invasion (Arikawa et al. 2002; Ong et al. 2002) Thus, evidence of clinically apparent skin infection may be a contraindication to occlusive therapy, as it may exacerbate the infection. (Aly et al. 1978) However, the possibility that *S. aureus* colonization

Another concern is that the use of topical corticosteroids under occlusion may relate to an increased potential for absorption and greater incidences of possible adverse effects. Most attention has been focused on the risk of skin atrophy and striae, hypothalamic-pituitary-

Ultimately, this chapter aims to examine current evidence on the safety and efficacy of

Studies on the use of occlusive therapy for the treatment of atopic dermatitis were identified in PubMed and Embase Medline databases from January 1966 to April 2011, using the key terms "occlusion," "occlusive dressings", "occlusive therapy," "wet wrap," "wet dressings," "dry wrap," "dry dressings," "atopic dermatitis," "dermatitis," and "eczema." Key terms were also searched in combination. Reference lists of relevant publications were manually searched for additional relevant studies. The search was limited to original studies and review articles published in English or with English abstracts, in humans. Studies of small size and those that did not use a controlled or randomized study design were included due to the dearth of published literature on this topic. Publications meeting these criteria were then reviewed for study design, population, disease severity or type, study size, efficacy, and safety. The topical agent used, dilution, and type and period of occlusive therapy were also noted, when such information was made available in the publication. In addition, response to therapy was seen as improvement in disease severity or symptoms from baseline, improvement in SCORing Atopic Dermatitis (SCORAD), and/or improvement in Eczema Area and Severity Index (EASI) score, depending on what information was provided. Of note, SCORAD is composite score of eczema severity based on the surface area involved, intensity of symptoms, and subjective symptoms such as sleep disturbance and pruritus. EASI is a 12-point scoring system of disease severity assessing erythema, induration, lichenification, pruritus, and excoriation. Finally, conclusions were drawn from

There are a total of 19 studies evaluating the use of occlusive therapy in AD (Table 1). Fourteen studies used WWD, 5 of which were randomized controlled trials. All WWD

may complicate occlusive therapy has not been adequately addressed to date.

adrenal (HPA) axis suppression, as well as growth impairment in children.

the results of these studies bearing in mind standard clinical practice.

Bridgman 1995; Krakowski et al. 2008)

occlusive therapy in the treatment of AD.

**3. Studies on occlusive therapy**

**2. Methods**

\*Dilution and concentration noted when provided in the article

Table 1. Studies on Occlusive Therapy (HCT = Hydrocortisone, RCT = randomized control trial)

Occlusive Therapy in Atopic Dermatitis 273

occlusion studies demonstrated efficacy in severe or acute, moderate and chronic AD. Among the 4 studies examining DWD, only one used a randomized controlled design. All, except one, DWD studies demonstrated improvements in AD. There is also one study that used an impermeable hydrogel patch consisting of about 50% water content. The hydrogel patch alone demonstrated improvements in AD, comparable to that of corticosteroid use alone. Increased cutaneous bacterial counts or clinical infections were reported in 4 out of

The following is a detailed description of the 14 studies evaluating the efficacy of WWD in the treatment of AD (Table 2). Occlusive therapy was first introduced by Goodyear et al. in 1991. Goodyear et al. (1991) evaluated the inpatient use of WWD occlusion for acute erythrodermic eczema. This WWD technique involved the application of open-weave cotton tubular dressings (Tubegauz) impregnanted with hydrocortisone 1% cream (if child <2 years of age) or 10% dilution of bemethasone valerate (if child > 2 years of age) twice daily. All 30 children responded well to WWD occlusion, with no relapses noted at 2 weeks follow-up. Interestingly, an attempt at long-term home therapy using WWD, following the inpatient therapy, in 5 patients was unsuccessful due to reports of inconvenience, increased

Mallon et al. (1994) studied the use of WWD in chronic severe eczema in 21 children. Eczema was managed using topical steroid creams (i.e. hydrocortisone 0.5% or 10% dilution betamethosone 0.1% cream) and emollients under WWD daily for less than 5 days. All patients responded well to WWD therapy. The treatment was also well-tolerated. Majority of parents (20/21) reported decreased use topical steroid per week following the

Abeck et al. (1999) treated 6 patients (3 children and 3 adults) with acute exacerbated atopic eczema with basic emollients in combination with chlorhexidine-soaked dressings for 3 days. The study observed improvements in disease severity based on SCORAD score. Patients also reported decreased itch and sleep loss following WWD therapy. In addition, there was a

In a study of 31 children with severe refractory AD, Wolkerstorfer et al. (2000) investigated the efficacy of various cortiocosteroid dilutions under WWD occlusion. Participants were divided into 3 treatment groups. The first group consisted of 18 children, who were treated with 50% dilution of fluticasone propionate 0.05% (FP) cream under WWD for 2 weeks. In the second group, 5 children with symmetrically localized AD were treated with different dilutions (10%, 25% and 50%) of FP cream on the left and the right side of the body under WWD for one week and then 10% dilution of FP cream under WWD the following week. In the third group, 8 children were treated with 0% (i.e. only emollient), 5%, 10%, or 25% dilutions of FP cream applied to the entire body under WWD. After just one week of therapy, significant improvement in disease severity was observed, without noticeable differences between 5%, 10%, or 25% dilutions of FP cream under WWD. Less improvement was observed in the second week of therapy. In terms of skin infections, mild-to-moderate folliculitis was reported in a large proportion of the children, with 33% (6/18) children in the first group, 40% (2/5) children in the second group, and 63% (5/8) children in the third group. There was also one case of furunculosis in the third group. Interestingly, generalized folliculitis was noted in both of the children treated with only emollient during the first week. These findings suggests that although WWD occlusion may foster bacterial growth,

bacterial infections, and prolonged HPA axis suppression. (Goodyear 1991)

reduction of *S. aureus* counts that paralleled skin improvement. (Abeck et al. 1999)

the 15 studies using WWD and all 4 studies using DWD.

introduction of WWD therapy. (Mallon et al. 1994)

**3.1 Wet wrap dressings**

\*Dilution and concentration noted when provided in the article

control trial)

Table 1. Studies on Occlusive Therapy (HCT = Hydrocortisone, RCT = randomized

occlusion studies demonstrated efficacy in severe or acute, moderate and chronic AD. Among the 4 studies examining DWD, only one used a randomized controlled design. All, except one, DWD studies demonstrated improvements in AD. There is also one study that used an impermeable hydrogel patch consisting of about 50% water content. The hydrogel patch alone demonstrated improvements in AD, comparable to that of corticosteroid use alone. Increased cutaneous bacterial counts or clinical infections were reported in 4 out of the 15 studies using WWD and all 4 studies using DWD.

#### **3.1 Wet wrap dressings**

The following is a detailed description of the 14 studies evaluating the efficacy of WWD in the treatment of AD (Table 2). Occlusive therapy was first introduced by Goodyear et al. in 1991. Goodyear et al. (1991) evaluated the inpatient use of WWD occlusion for acute erythrodermic eczema. This WWD technique involved the application of open-weave cotton tubular dressings (Tubegauz) impregnanted with hydrocortisone 1% cream (if child <2 years of age) or 10% dilution of bemethasone valerate (if child > 2 years of age) twice daily. All 30 children responded well to WWD occlusion, with no relapses noted at 2 weeks follow-up. Interestingly, an attempt at long-term home therapy using WWD, following the inpatient therapy, in 5 patients was unsuccessful due to reports of inconvenience, increased bacterial infections, and prolonged HPA axis suppression. (Goodyear 1991)

Mallon et al. (1994) studied the use of WWD in chronic severe eczema in 21 children. Eczema was managed using topical steroid creams (i.e. hydrocortisone 0.5% or 10% dilution betamethosone 0.1% cream) and emollients under WWD daily for less than 5 days. All patients responded well to WWD therapy. The treatment was also well-tolerated. Majority of parents (20/21) reported decreased use topical steroid per week following the introduction of WWD therapy. (Mallon et al. 1994)

Abeck et al. (1999) treated 6 patients (3 children and 3 adults) with acute exacerbated atopic eczema with basic emollients in combination with chlorhexidine-soaked dressings for 3 days. The study observed improvements in disease severity based on SCORAD score. Patients also reported decreased itch and sleep loss following WWD therapy. In addition, there was a reduction of *S. aureus* counts that paralleled skin improvement. (Abeck et al. 1999)

In a study of 31 children with severe refractory AD, Wolkerstorfer et al. (2000) investigated the efficacy of various cortiocosteroid dilutions under WWD occlusion. Participants were divided into 3 treatment groups. The first group consisted of 18 children, who were treated with 50% dilution of fluticasone propionate 0.05% (FP) cream under WWD for 2 weeks. In the second group, 5 children with symmetrically localized AD were treated with different dilutions (10%, 25% and 50%) of FP cream on the left and the right side of the body under WWD for one week and then 10% dilution of FP cream under WWD the following week. In the third group, 8 children were treated with 0% (i.e. only emollient), 5%, 10%, or 25% dilutions of FP cream applied to the entire body under WWD. After just one week of therapy, significant improvement in disease severity was observed, without noticeable differences between 5%, 10%, or 25% dilutions of FP cream under WWD. Less improvement was observed in the second week of therapy. In terms of skin infections, mild-to-moderate folliculitis was reported in a large proportion of the children, with 33% (6/18) children in the first group, 40% (2/5) children in the second group, and 63% (5/8) children in the third group. There was also one case of furunculosis in the third group. Interestingly, generalized folliculitis was noted in both of the children treated with only emollient during the first week. These findings suggests that although WWD occlusion may foster bacterial growth,

#### 274 Atopic Dermatitis – Disease Etiology and Clinical Management Occlusive Therapy in Atopic Dermatitis 275

Table 2. Outcomes of Studies on Wet Wrap Dressing Occlusion (DPD = deoxypyridinoline,

HPA = hypothalamic-pituitary-adrenal, HRQoL = Health Related Quality of Life)

Table 2. Outcomes of Studies on Wet Wrap Dressing Occlusion (DPD = deoxypyridinoline, HPA = hypothalamic-pituitary-adrenal, HRQoL = Health Related Quality of Life)

cheek in a patient without a facial mask, and purulent conjunctivitis in a patient with a facial mask. These complications may be attributed to variations in standard protocal for WWD application, such as prolonged (>8 hours) occlusion and the frequent rewetting procedure.

McGowan et al. (2003) examined the effects of WWD therapy using topical corticosteroids on short-term growth and bone turnover in 8 prepubertal children, ranging from 3-8 years of age. Tubular bandages were applied over 10% or 25% dilutions of beclomethasone dipropionate for 24 hours each day for 2 weeks. After 2 weeks, frequency of tubular bandages was reduced to overnight use for one week and then as required for the remainder of the treatment period. Occlusive dressings were applied for a median duration of 12 weeks (range 2 – 18 weeks). Short-term growth was assessed by measuring lower leg length velocity by knemometry, while bone turnover was assessed by urinary deoxypyridinoline excretion. (McGowan et al. 2003) (See Section 3.4 Cutaneous and Systemic Side Effects for

In randomized control trial, Beattie and Lewis-Jones (2004) compared the use of 1% hydrocortisone under WWD to conventional open therapy in 19 children with moderate, widespread AD. The control group applied 1% hydrocortisone twice daily for 2 weeks, without WWD. In the study group, patients applied 1% hydrocortisone once in the morning for 2 weeks, with WWD twice daily for the first week and then only at night for the second week. Both groups were allowed to apply non-steroidal emollients as often as necessary. Beattie and Lewis Jones (2004) found no difference in clinical improvement between the control group and the study group. The authors, therefore, concluded that conventional open therapy using 1% hydrocortisone and emollients alone appeared to be as effective as using 1% hydrocortisone under WWD for moderate AD. Despite these findings, it is important to note that the use of 1% hydrocortisone is a less potent choice than what is generally used in clinical practice when treating moderate AD. If the authors had evaluated the use of a mid-potency topical corticosteroid under WWD, the degree of improvement between the study and control groups might have been markedly different. In terms of health related quality of life, Beattie and Lewis-Jones (2004) found greater improvements in the non-WWD control group than the WWD group for both the child and the family. Children in the non-WWD control group also reported more sleep than the WWD group, but there was no significant difference for itch between treatment groups. In regards to infections, 2 of the 10 (20%) children in the WWD group experienced folliculitis, one of which had to be withdrawal from the study. There were no reported clinical infections in the

Foelster-Holst et al. (2006) conducted a randomized, controlled study of 24 adults and children with acute episodes of AD. This was left-right comparison study, in which patients had skin lesions symmetrically affecting both arms or legs. One arm or leg was randomly treated with the topical prednicarbat (a medium potency corticosteroid), with WWD using a tubular bandage. The other extremity received topical prednicarbat alone. After 48-72 hours of therapy, both groups showed improvement of the local SCORAD, but the improvement in the WWD group was significantly better. No adverse effects were observed in either

Hindley et al. (2006) carried a randomized, control trial to investigate the efficacy of WWD as compared to conventional topically applied corticosteroids. This 4-week study consisted of a total of 50 children with moderate-to-severe eczema. In the conventional treatment group, patients had emollients applied as needed and 1% hydrocortisone ointment (or more

(Devillers et al. 2002)

further discussion of this study)

non-WWD control group. (Beattie and Lewis-Jones 2004)

treatment group. (Foelster-Holst et al. 2006)

the addition of topical corticosteroids to the treatment regimen appeared to provide some protective benefits. (Wolkerstorfer et al. 2000)

Tang (2000) treated 10 children experiencing a flare of facial eczema with WWD occlusion. Children were initiated on an intermittent treatment regimen involving 10% dilution of mometasone furoate 0.1% cream or ointment under WWD applied for 2-3 hours once daily for a few consecutive days. All parents reported good treatment response. No cutaneous side effects were observed from topical corticosteroid use. (Tang 2000)

Pei et al. (2001) performed a randomized control trial of 40 children with moderate-to-severe AD. Prior to starting the study, all patient were instructed to apply 0.005% flucinolone acetonide cream twice daily for 2 weeks to standardize treatment medications. Patient were then randomized to receive 10% dilution of 0.1% mometasone furoate ointment or 10% dilution of 0.005% fluticasone propionate ointment. These topical agents were applied once a day for 2 weeks without WWD. After this 2-week period of open application, patients were further randomized to receive the same topical agent for 2 more weeks without WWD, or for 2 more weeks under WWD. Only 30 patients (75%) entered into this second phase of the study since their disease severity had failed to improve by more than 50% after the initial 2 weeks of open topical application. In other words, only patients whose disease was refractory to a 2-week period of conventional open therapy continued in the study. Ultimately, there were a total of 27 patients who completed the study. One child receiving fluticasone propionate ointment dropped out of the study because the patient was unable to tolerate WWD. The study found that significantly greater improvements in disease severity and extent in patients using WWD, as compared to controls. These results suggest that WWD may be an effective second-line therapy in children whose disease is refractory to conventional open topical corticosteroids. (Pei et al. 2001)

Schnopp et al. (2002) examined the effect of WWD in a randomized control study of 20 inpatients with exacerbated AD. Children received either a topical corticosteroid preparation (mometasone furoate 0.1%) or a steroid-free preparation (its vehicle) under WWD, applied twice daily for 5 days to the tested area in a left-right study. Disease severity at day 3 and day 5 continuously improved in both groups; however, the mometasone furoate-treated group showed significantly greater irmprovements. *Staphylococcus aureus* bacterial counts initially decreased during the first 3 days of treatment in both groups. At day 5, bacterial counts continued to decrease in the steroid-treated group, but bacterial counts increased in the vehicle-treated group. There were no reported clinical signs of bacterial superinfection in either the steroid or vehicle groups. The study concluded that WWD were useful in treatment of exacerbated AD, with applications of topical corticosteroids showing better efficacy than steroid-free emollients. (Schnopp et al. 2002)

Devillers et al. (2002) evaluated the use of WWD in refractory AD in 12 adults and 14 children. WWD were applied daily and re-wettted every 2-3 hours for 1 week in an inpatient setting. Patients used 5% dilution of FP cream under WWD on affected areas of the face. As for the body, a side-to-side comparison study was performed, in which adults applied 10% and 25% dilutions of FP cream and children applied 5% and 10% dilutions of FP cream. Disease severity improved dramatically during the one week of inpatient therapy. There was no difference in improvement between dilutions applied to each side of the body. Following inpatient therapy, 8 adults and 13 children continued treatment at home with less potent dilutions of FP cream. Exacerbation of AD occurred in 3 adults and 2 children. Infectious complications included localized folliculitis (4 reported cases), secondary impetigo (2 reported cases), localized *Pseudomonas aeruginosa* infection, cellulitis of the left

the addition of topical corticosteroids to the treatment regimen appeared to provide some

Tang (2000) treated 10 children experiencing a flare of facial eczema with WWD occlusion. Children were initiated on an intermittent treatment regimen involving 10% dilution of mometasone furoate 0.1% cream or ointment under WWD applied for 2-3 hours once daily for a few consecutive days. All parents reported good treatment response. No cutaneous

Pei et al. (2001) performed a randomized control trial of 40 children with moderate-to-severe AD. Prior to starting the study, all patient were instructed to apply 0.005% flucinolone acetonide cream twice daily for 2 weeks to standardize treatment medications. Patient were then randomized to receive 10% dilution of 0.1% mometasone furoate ointment or 10% dilution of 0.005% fluticasone propionate ointment. These topical agents were applied once a day for 2 weeks without WWD. After this 2-week period of open application, patients were further randomized to receive the same topical agent for 2 more weeks without WWD, or for 2 more weeks under WWD. Only 30 patients (75%) entered into this second phase of the study since their disease severity had failed to improve by more than 50% after the initial 2 weeks of open topical application. In other words, only patients whose disease was refractory to a 2-week period of conventional open therapy continued in the study. Ultimately, there were a total of 27 patients who completed the study. One child receiving fluticasone propionate ointment dropped out of the study because the patient was unable to tolerate WWD. The study found that significantly greater improvements in disease severity and extent in patients using WWD, as compared to controls. These results suggest that WWD may be an effective second-line therapy in children whose disease is refractory to

Schnopp et al. (2002) examined the effect of WWD in a randomized control study of 20 inpatients with exacerbated AD. Children received either a topical corticosteroid preparation (mometasone furoate 0.1%) or a steroid-free preparation (its vehicle) under WWD, applied twice daily for 5 days to the tested area in a left-right study. Disease severity at day 3 and day 5 continuously improved in both groups; however, the mometasone furoate-treated group showed significantly greater irmprovements. *Staphylococcus aureus* bacterial counts initially decreased during the first 3 days of treatment in both groups. At day 5, bacterial counts continued to decrease in the steroid-treated group, but bacterial counts increased in the vehicle-treated group. There were no reported clinical signs of bacterial superinfection in either the steroid or vehicle groups. The study concluded that WWD were useful in treatment of exacerbated AD, with applications of topical corticosteroids showing better efficacy than steroid-free emollients. (Schnopp et al. 2002) Devillers et al. (2002) evaluated the use of WWD in refractory AD in 12 adults and 14 children. WWD were applied daily and re-wettted every 2-3 hours for 1 week in an inpatient setting. Patients used 5% dilution of FP cream under WWD on affected areas of the face. As for the body, a side-to-side comparison study was performed, in which adults applied 10% and 25% dilutions of FP cream and children applied 5% and 10% dilutions of FP cream. Disease severity improved dramatically during the one week of inpatient therapy. There was no difference in improvement between dilutions applied to each side of the body. Following inpatient therapy, 8 adults and 13 children continued treatment at home with less potent dilutions of FP cream. Exacerbation of AD occurred in 3 adults and 2 children. Infectious complications included localized folliculitis (4 reported cases), secondary impetigo (2 reported cases), localized *Pseudomonas aeruginosa* infection, cellulitis of the left

side effects were observed from topical corticosteroid use. (Tang 2000)

conventional open topical corticosteroids. (Pei et al. 2001)

protective benefits. (Wolkerstorfer et al. 2000)

cheek in a patient without a facial mask, and purulent conjunctivitis in a patient with a facial mask. These complications may be attributed to variations in standard protocal for WWD application, such as prolonged (>8 hours) occlusion and the frequent rewetting procedure. (Devillers et al. 2002)

McGowan et al. (2003) examined the effects of WWD therapy using topical corticosteroids on short-term growth and bone turnover in 8 prepubertal children, ranging from 3-8 years of age. Tubular bandages were applied over 10% or 25% dilutions of beclomethasone dipropionate for 24 hours each day for 2 weeks. After 2 weeks, frequency of tubular bandages was reduced to overnight use for one week and then as required for the remainder of the treatment period. Occlusive dressings were applied for a median duration of 12 weeks (range 2 – 18 weeks). Short-term growth was assessed by measuring lower leg length velocity by knemometry, while bone turnover was assessed by urinary deoxypyridinoline excretion. (McGowan et al. 2003) (See Section 3.4 Cutaneous and Systemic Side Effects for further discussion of this study)

In randomized control trial, Beattie and Lewis-Jones (2004) compared the use of 1% hydrocortisone under WWD to conventional open therapy in 19 children with moderate, widespread AD. The control group applied 1% hydrocortisone twice daily for 2 weeks, without WWD. In the study group, patients applied 1% hydrocortisone once in the morning for 2 weeks, with WWD twice daily for the first week and then only at night for the second week. Both groups were allowed to apply non-steroidal emollients as often as necessary. Beattie and Lewis Jones (2004) found no difference in clinical improvement between the control group and the study group. The authors, therefore, concluded that conventional open therapy using 1% hydrocortisone and emollients alone appeared to be as effective as using 1% hydrocortisone under WWD for moderate AD. Despite these findings, it is important to note that the use of 1% hydrocortisone is a less potent choice than what is generally used in clinical practice when treating moderate AD. If the authors had evaluated the use of a mid-potency topical corticosteroid under WWD, the degree of improvement between the study and control groups might have been markedly different. In terms of health related quality of life, Beattie and Lewis-Jones (2004) found greater improvements in the non-WWD control group than the WWD group for both the child and the family. Children in the non-WWD control group also reported more sleep than the WWD group, but there was no significant difference for itch between treatment groups. In regards to infections, 2 of the 10 (20%) children in the WWD group experienced folliculitis, one of which had to be withdrawal from the study. There were no reported clinical infections in the non-WWD control group. (Beattie and Lewis-Jones 2004)

Foelster-Holst et al. (2006) conducted a randomized, controlled study of 24 adults and children with acute episodes of AD. This was left-right comparison study, in which patients had skin lesions symmetrically affecting both arms or legs. One arm or leg was randomly treated with the topical prednicarbat (a medium potency corticosteroid), with WWD using a tubular bandage. The other extremity received topical prednicarbat alone. After 48-72 hours of therapy, both groups showed improvement of the local SCORAD, but the improvement in the WWD group was significantly better. No adverse effects were observed in either treatment group. (Foelster-Holst et al. 2006)

Hindley et al. (2006) carried a randomized, control trial to investigate the efficacy of WWD as compared to conventional topically applied corticosteroids. This 4-week study consisted of a total of 50 children with moderate-to-severe eczema. In the conventional treatment group, patients had emollients applied as needed and 1% hydrocortisone ointment (or more

(available since 2003). With the introduction of these garments, wet wrapping can be done in 20–25 minutes. Tubifast garments® are available as tights for babies aged 6–24 months, vests for children 6 months through 14 years, and socks and leggings in all sizes. These washable garments are absorbent, holding enough water to remain moist for hours, and are elastic

1. Choose the appropriate width of the tubular bandages and cut these to size to fit the affected body areas (i.e. arms, legs, trunk). Alternatively, Tubifast® garments

2. Apply the appropriate dilution of topical corticosteroids (e.g. fluticasone propionate 0.05% cream, mometasone furoate 0.1% cream) on the involved skin. In general, diluted steroids in emollients of 1:9 are applied to the face of all patients and body of infants, while diluted steroids in emollients of 1:9 or 1:3 are applied on the body of adults. 3. Wet the pieces of tubular bandage in lukewarm water. Alternatively, if Tubifast® garments are used, then the inner garment is moistened using a plant sprayer. 4. Apply the first layer of wet tubular bandages. Connect the arm and leg pieces to the trunk. Apply the facial mask, if necessary. Alternatively, if Tubifast® garments are

5. Apply the second layer of dry tubular bandage. Again, connect the arm and leg pieces to the trunk. Apply the facial mask, if necessary. Alternatively, if Tubifast® garments are used, a second dry Tubifast® garment is placed over the wet one. 6. Re-wet the tubular bandages every 2-3 hours. Alternatively, if Tubifast® garments

8. After 7 days of occlusive therapy, the dilution of topical corticosteroids (e.g. fluticasone propionate 0.05% cream, mometasone furoate 0.1% cream) is applied on

Finally, in a review article, Devillers and Oranje (2006) made the following conclusions regarding WWD occlusion with a grade C of recommendation. 1) WWD using cream or ointment and a double layer of cotton bandages, with a moist first layer and a dry second layer, is an efficacious short-term treatment for children with severe and/or refractory AD.2) The use of WWD with diluted topical corticosteroids is a more efficacious treatment than wet-wrap dressings with emollients only for children with severe and/or refractory AD. 3) The use of WWD with diluted topical corticosteroids is a safe intervention treatment for children with severe and/or refractory AD for up to 14 days, with temporary systemic bioactivity of the corticosteroids as the only reported serious adverse effect. 4) Lowering the absolute amount of applied topical corticosteroid to once daily application and further

DWD occlusion in AD has been less well studied (Table 4). Specifically, Rajka et al. (1981) examined the effect of dry occlusion on skin microbial flora. Occlusion using plastic film was applied to 10 patients with AD. A significant increase in the density of *S. aureus* was observed after 24 hours of dry occlusion. Notably, 2 of the 10 patients had tiny pustules or crusts following dry occlusion. But, there were no reports of AD exacerbation. (Rajka et al. 1981)

and able to conform to the contours of the body. (Page 2005)

used, the inner garment is moistened using a plant spray.

are used, re-wet the inner Tubifast® garment every 2-3 hours.

7. Repeat procedures #1-6 (described above) daily.

the involved skin for 4-7 consecutive days.

dilution can reduce potential risks. (Devillers and Oranje 2006)

Table 3. Protocol for Wet Wrap Dressing occlusion

can be used.

**3.2 Dry wrap dressings**

potent topical steroids, if necessary) applied twice daily. In the WWD treatment group, patients had wet wraps applied daily for a 24-hour period over 1% hydrocortisone ointment (or more potent topical steroids, if necessary) during the first week, followed by wet wraps applied for a 12- or 24-hour period depending on disease progress for the remaining three weeks. When wet wraps were applied for only a 12-hour period, 1% hydrocortisone and emollients were used during the non-wet wrap period. Both treatment groups demonstrated improvement in overall SCORAD scores; however, there was no significant difference between the conventional and WWD treatment groups. Five out of 23 (22%) children in the WWD treatment group required antibiotics for skin infections, as compared to none of the children in the conventional treatment group. The authors conclude that 4-weeks of maintenance WWD treatment may be associated with more skin infections than conventional treatment. (Hindley et al. 2006) However, it is important to realize that in clinical practice, physicians usually do not use WWD for maintenance therapy of AD over a 4-week duration. Instead, physicians are more likely to use WWD in settings of acute generalized eczematous flares for 3-7 days to induce disease remission. (Williams 2006) Lee et al. (2007) examined the therapeutic efficacy of WWD and the mechanism behind its therapeutic efficacy in treatment of AD. Ten patients with severe AD received WWD (without steroid treatment) for 7–14 days. SCORAD was used to assess AD severity, immediately following the end of treatment and 7 days after termination of treatment. Transepidermal water loss, water content in the corneum, and lipid amount of skin surface were also measured. The SCORAD was significantly reduced after WWD therapy. Additionally, epidermal water content was increased and transepidermal water loss was decreased following WWD therapy; these results were maintained 1 week after terminating therapy. In atopic lesions, increased release of lamellar bodies and restoration of intercellular lipid lamellar structure was observed. The authors speculated that increased secretion of lamellar bodies induced with WWD occlusion may lead to recovery of the abnormal epidermal barrier and clinical improvement in AD. (Lee et al. 2007)

In a clinical study of six children with moderate to severe AD, Hon et al. (2007) tested the efficiacy of WWD occlusion using Tubifast® garments with mometasone furoate 0.1% cream. Short-term use of WWD occlusion over 3 days demonstrated improvement in disease severity based on SCORAD. In addition, a wrist motion monitor was used to measure nocturnal itch, which showed that average scratching activity was significantly reduced by 20–60% on day 3 of treatment. Furthermore, WWD was effective in improving quality of life in these children. (Hon et al. 2007)

Since its introduction by Goodyear et al. (1991) nearly two decades ago, WWD occlusion has been extensively used as a relatively safe and effective treatment modality for children with acute erythrodermic AD and those with severe and/or refractory AD. The most effective topical corticosteroid to be used is still uncertain, but 10% dilutions of potent topical corcorticosteroid are most commonly used. Protocols on adminstration and duration of WWD occlusion can vary between studies. (Oranje et al. 2006) (See Table 3)

Advantages of WWD occlusion include a rapid therapeutic response, reduction in itch and sleep disturbances, and a possible decreased topical corticosteroid use. Disadvantages include high cost, the need for specialized training, increased potential for topical corticosteroid absorption, and increased incidences of folliculitis and other cutaneous infections. (Oranje et al. 2006)

However, the application of WWD has become less time-consuming and more feasible for home use with development of Tubifast® garments manufactured by Medlock Medical®

potent topical steroids, if necessary) applied twice daily. In the WWD treatment group, patients had wet wraps applied daily for a 24-hour period over 1% hydrocortisone ointment (or more potent topical steroids, if necessary) during the first week, followed by wet wraps applied for a 12- or 24-hour period depending on disease progress for the remaining three weeks. When wet wraps were applied for only a 12-hour period, 1% hydrocortisone and emollients were used during the non-wet wrap period. Both treatment groups demonstrated improvement in overall SCORAD scores; however, there was no significant difference between the conventional and WWD treatment groups. Five out of 23 (22%) children in the WWD treatment group required antibiotics for skin infections, as compared to none of the children in the conventional treatment group. The authors conclude that 4-weeks of maintenance WWD treatment may be associated with more skin infections than conventional treatment. (Hindley et al. 2006) However, it is important to realize that in clinical practice, physicians usually do not use WWD for maintenance therapy of AD over a 4-week duration. Instead, physicians are more likely to use WWD in settings of acute generalized eczematous flares for 3-7 days to induce disease remission. (Williams 2006) Lee et al. (2007) examined the therapeutic efficacy of WWD and the mechanism behind its therapeutic efficacy in treatment of AD. Ten patients with severe AD received WWD (without steroid treatment) for 7–14 days. SCORAD was used to assess AD severity, immediately following the end of treatment and 7 days after termination of treatment. Transepidermal water loss, water content in the corneum, and lipid amount of skin surface were also measured. The SCORAD was significantly reduced after WWD therapy. Additionally, epidermal water content was increased and transepidermal water loss was decreased following WWD therapy; these results were maintained 1 week after terminating therapy. In atopic lesions, increased release of lamellar bodies and restoration of intercellular lipid lamellar structure was observed. The authors speculated that increased secretion of lamellar bodies induced with WWD occlusion may lead to recovery of the

abnormal epidermal barrier and clinical improvement in AD. (Lee et al. 2007)

WWD occlusion can vary between studies. (Oranje et al. 2006) (See Table 3)

in these children. (Hon et al. 2007)

infections. (Oranje et al. 2006)

In a clinical study of six children with moderate to severe AD, Hon et al. (2007) tested the efficiacy of WWD occlusion using Tubifast® garments with mometasone furoate 0.1% cream. Short-term use of WWD occlusion over 3 days demonstrated improvement in disease severity based on SCORAD. In addition, a wrist motion monitor was used to measure nocturnal itch, which showed that average scratching activity was significantly reduced by 20–60% on day 3 of treatment. Furthermore, WWD was effective in improving quality of life

Since its introduction by Goodyear et al. (1991) nearly two decades ago, WWD occlusion has been extensively used as a relatively safe and effective treatment modality for children with acute erythrodermic AD and those with severe and/or refractory AD. The most effective topical corticosteroid to be used is still uncertain, but 10% dilutions of potent topical corcorticosteroid are most commonly used. Protocols on adminstration and duration of

Advantages of WWD occlusion include a rapid therapeutic response, reduction in itch and sleep disturbances, and a possible decreased topical corticosteroid use. Disadvantages include high cost, the need for specialized training, increased potential for topical corticosteroid absorption, and increased incidences of folliculitis and other cutaneous

However, the application of WWD has become less time-consuming and more feasible for home use with development of Tubifast® garments manufactured by Medlock Medical® (available since 2003). With the introduction of these garments, wet wrapping can be done in 20–25 minutes. Tubifast garments® are available as tights for babies aged 6–24 months, vests for children 6 months through 14 years, and socks and leggings in all sizes. These washable garments are absorbent, holding enough water to remain moist for hours, and are elastic and able to conform to the contours of the body. (Page 2005)

Table 3. Protocol for Wet Wrap Dressing occlusion

Finally, in a review article, Devillers and Oranje (2006) made the following conclusions regarding WWD occlusion with a grade C of recommendation. 1) WWD using cream or ointment and a double layer of cotton bandages, with a moist first layer and a dry second layer, is an efficacious short-term treatment for children with severe and/or refractory AD.2) The use of WWD with diluted topical corticosteroids is a more efficacious treatment than wet-wrap dressings with emollients only for children with severe and/or refractory AD. 3) The use of WWD with diluted topical corticosteroids is a safe intervention treatment for children with severe and/or refractory AD for up to 14 days, with temporary systemic bioactivity of the corticosteroids as the only reported serious adverse effect. 4) Lowering the absolute amount of applied topical corticosteroid to once daily application and further dilution can reduce potential risks. (Devillers and Oranje 2006)


**8. References**

FCC (2002). Federal Communications Commission, FCC 02-48, ET-Docket 98-153, "*First Report and Order"*, Apr. 2002.

182 Ultra Wideband – Current Status and Future Trends

*International Research Centre for Telecommunication and Radar(IRCTR), Netherlands*

The research reported in this work was effectuated with in the frame of the "Wise Band Sparse Element Array Antennas" WiSE-project, a scientific undergone financed by the Dutch Technology Foundation (Stichting Technische Wetenschapen – STW). This support is hereby gratefully acknowledged. This technological-transfer is made possible to the "Sensor Technology Applied in Reconfigurable Systems for Sustainable Security" STARS-project thanks to the successful collaboration between two national institutions IRCTR (Netherlands), and METRA (Romania), with Thales, TNO, ASTRON and ESA as

Abbosh, A.M. et al. (2007), Design of a high fidelity UWB planar antenna operating in a high dielectric medium, Proceed. of the IEEE Ant. and Prop. Soc. Int. Symp. 9-15 Jun. 2007,

Balanis, C.A.(1997). Antenna theory analysis and design, Wiley Inc, 2nd ed. New York, 1997. Bataller, M.F. et al.(2006), An overview of planar monopole antennas for UWB application,

Biscontini, B. et al.(2006), A Novel Multilayered Planar Antenna for Ultra Wide Band (UWB) Intelligent Antenna Systems, Proc. of the 22nd Ann. Rev. of Prog. in Appl. Comp.

Brown, D., Fiscus, T.E, Meierbachtol, C.J(1980). Results of a study using RT 5880 material for a missile radome, In: Symp. on Electromagnetic Windows, 15th, Atlanta, GA, June 18-

Chavka, G. et al.(2006), "Radiation of ultra-wideband signals by pulse antenna" in proceeding of the Ultra-wideband and Ultra-short Impulse Signals, 18-22 September,

Chiou, J.Y. et al.(2003), A Broad-Band CPW-Fed Strip-Loaded Square Slot Antenna, IEEE Transactions on Antennas and Propagation, Vol. 51, No. 4, April 2003, pp.719-721. Cho, Y.J. et al.(2006), A Miniature UWB Planar Monopole Antenna With 5-GHz Band-Rejection Filter and the Time-Domain Characteristics, IEEE Trans. AP. Vol.54, No. 5,

Choi, S.H. et al.(2004), A new ultra-wideband antenna for UWB applications, MOTL, V.40,

Choi, S.T. et al.(2009), Small printed CPW-fed triangular monopole antenna for ultrawideband applications, IEEE Micro & Opt. Tech. Letters, Vol.51, No.5, May

Electromagnetics ACES, March 12-16, 2006, Miami, FL; pp. 198 - 204.

20, Proc. (A82-2645, 11-32), Georgia Inst. of Technology, p.7-12.

*Military Equipment and Technologies Research Agency, Romania*

A. Szilagyi

**Acknowledgement**

technological supervisory bodies.

Honolulu, USA, pp.241-244.

2006, Sevastopol, Ukraine.

May 2006.pp-1453-1460.

No.5, Mar. 2004

2009,pp.180-182.

Proc Eucap 2006, Nov. Nice , France

**8. References**

Shastry, P.N. et al.(2009), Planar UWB Conical Skirt Tapered Monopole Antenna; Proceed. of the 9th IEEE Wireless and Micr. Tech. Conf., WAMICON'09. 20-21 April 2009.

**Chapter 9**

© 2012 Malayeri, licensee InTech. This is an open access chapter 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.

© 2012 Malayeri, licensee InTech. This is a paper 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.

UWB technology is advancing rapidly because of its potential to have high data rates and very low radiation power. In recent years UWB technology has been used in the areas of, sensing, radar and military communications [1]. In February 2002, the Federal Communications Commission (FCC) of the United States issued a report that UWB could be used for wireless data Communications [2]. Since then, a huge surge of research interests have occurred and this technology has been considered as one of the most reliable wireless technologies for various applications that leads to new innovations and greater quality of

Reliable wireless connection between computers, portable devices and consumer electronics in short distances and data storage and transfer between these devices are new subjects of scientific and industrial competitions which require data rates much more than now a day

In this chapter, at the second part, some advantages of ultra-wideband technology and its progress trend will be reviewed. In the third part, antennas structures and parameters, especially wideband antennas will be studied for use in the UWB systems. To describe the performance of an antenna, various parameters must be defined. There are several important and practical parameters such as frequency bandwidth, radiation pattern, directivity, gain and input impedance which will be explained briefly. The performance of a UWB antenna is required to be stable and uniform over the ultra wide operational bandwidth. In the other word, antenna radiation pattern, gain and input impedance should be stable across the entire band. Also antenna needs to be small enough to be compatible with the other UWB system elements, especially in portable devices. In addition, basic antenna parameters, such as gain and return loss, must have little variations across the

**Active Integrated Antenna**

Additional information is available at the end of the chapter

wireless personal area network services industry.

Danial Nezhad Malayeri

http://dx.doi.org/10.5772/50185

**1. Introduction**

accessible ones.

**Design for UWB Applications**

European conference on wireless technology, pp.40-43, Munich, Germany, Oct.8-10, 2007.

**Chapter 9**


**3. Human dietary lipid digestion process and regulation of pancreatic fluid in healthy state**

Protein digestion begins in the stomach with the concomitant action of hydrochloric acid and pepsin, continues with pancreatic proteases in the duodenum, and finishes with numerous brush border peptidases located all over the small intestine (Fieker & al., 2011 as cited in Alpers, 1994). Starch digestion begins in the mouth with salivary amylase, continues with pancreatic amylase, and ends with several intestinal brush border oligosaccharidases (Fieker & al., 2011 as cited in Alpers, 1994). In contrast, the majority of lipid digestion and absorption occurs between the pylorus and the ligament of Treitz. Prior to this step, 5% to 40% of the dietary triglyceride acyl chains are released in the stomach by gastric lipase (Armand & al., 1994, 1996, 1999; Carrière & al., 1993b ; Hamosh, 1990) which continues its action in the duodenum together with pancreatic lipase until these enzymes are degraded by pancreatic proteases. Although a pH of 8 to 9 appears to be optimal for pancreatic lipase activity *in vitro*, bile salts allow the enzyme to work efficiently at a pH of 6 to 6.5 *in vivo* (Borgstrom, 1964; Carrière & al., 2005). HPL is responsible for the hydrolysis of 40% to 70% of triglycerides (Fig.2).

The pancreatic lipase-related 2 protein (hPLRP2), with a broader substrate specificity, hydrolyzes milk triglycerides (Berton & al., 2009) phospholipids (Jayne & al., 2002; Lowe, 2002; Thirstrup & al., 1994) galactolipids (Sias & al., 2004) and esters of lipid-soluble vitamins (Reboul & al., 2006). Carboxyl ester lipase (also called bile salt-stimulated lipase,

Emerging Approaches for the Treatment of

Fat Malabsorption due to Exocrine Pancreatic Insufficiency 277

Solomon, 1994). This gastric phase of digestion represents an important aspect in the overall postprandial regulation of pancreatic secretion. During the intestinal phase, enterohormones, such as CCK, together with neurotransmitters and neuropeptides further stimulate pancreatic secretion (Chey & Chang, 2001). Thus, digestive pancreatic enzyme response to a meal follows a specific pattern in which the degree and duration depend on nutrient composition, caloric content and physical properties of the meal. Enzyme secretion into the duodenum increases quickly reaching peak output within the first 20 to 60 minutes postprandially, then decreasing to a stable level before reaching an interdigestive level at the

end of the digestive period, ie, about 4 hours after meal intake (Keller & Layer, 2005).

leading role in the digestion of fat, which is the highest dietary source of calories.

occurs primarily in disorders directly affecting pancreatic tissue integrity (Table 3).

As previously described, the pancreas functions as the main factory for the digestive enzymes. The gland produces pancreatic juice that consists of a mixture of more than two dozen digestive enzymes in the pre-activated form, called zymogens. Zymogens are produced by acinar cells and mixed with a bicarbonate rich fluid that is produced by pancreatic ducts cells (Whitcomb & Lowe, 2007). Trypsin, chymotrypsin, amylase and lipase are responsible for the majority of the enzyme activity derived from the pancreas (Whitcomb & Lowe, 2007). Lipase is one of the most important enzymes because it plays a

Pancreatic exocrine insufficiency, partial or complete loss of digestive enzyme synthesis,

Pancreatic parenchymal disease

Chronic pancreatitis Post-necrotizing acute pancreatitis Cystic fibrosis Pancreatic cancers/tumors Autoimmune pancreatitis Extrapancreatic disease

Celiac disease Inflammatory bowel disease Diabetes mellitus Zollinger-Ellison syndrome

Postsurgical states

Gastric resection Whipple's pancreaticoduodenectomy Short bowel syndrome Bariatric surgeries (eg, gastric bypass)

Table 3. Conditions Causing EPI (adapted from Keller et al., 2009).

**4. Exocrine pancreatic insufficiency & fat malabsorption**

Fig. 2. Schematic representation of the relative contributions of HGL and HPL to the overall digestion of dietary triacylglycerides. On a weight basis, the ratio of pancreatic lipase to gastric lipase total secretory outputs was found to be around four after 3 hours of digestion. The level of gastric hydrolysis was calculated to be 10% of the acyl chains released from the meal triglycerides. Gastric lipase remained active in the duodenum where it might still hydrolyze 7.5% of the triglyceride acyl chains. Hence, globally, during the whole digestion period, gastric lipase hydrolyzes 17.5% of all the triglyceride acyl chains. (Reproduced from Carrière & al., 1993b).

(BSSL)) will hydrolyze triglycerides, diglycerides, phospholipids, and esters of lipid-soluble vitamins and of cholesterol (Hui & Howles, 2002). Phospholipase A2 hydrolyzes phospholipids to lysophospholipids20 which is essential for an optimal absorption of lipid nutrients (Fieker & al., 2011, as cited in Tso, 1994).

Products generated during lipolysis are solubilized in bile salts–mixed micelles and liposomes (vesicles) which allow absorption across the intestinal villi. Once absorbed, the digested lipids are converted back to triglycerides, phospholipids, and esters of cholesterol and of lipid-soluble vitamins, then packaged as chylomicrons and transported through the thoracic duct into the systemic circulation for delivery to various sites throughout the body (Fieker & al., 2011, as cited in Tso, 1994).

To execute this digestive function, postprandial pancreatic juice secretion can increase up to 1 to 2 L per day in response to physiologic stimuli, mainly secretin and vagal output (Lee & Muallem, 2009). Appropriate enzyme delivery in the duodenum is allowed through a specific orchestration of the pancreatic fluid secretion during the fed state. In fact, during the gastric phase, digestion of proteins by pepsin and of triglycerides by gastric lipase generates amino acids and free fatty acids, respectively (Fieker & al., 2011, as cited in Alpers, 1994). When delivered through the pylorus, they become powerful stimulants of the cholecystokinin hormone (CCK) produced by the duodenal endocrine cells which stimulates pancreatic enzymes secretion and controls the gastric emptying rate. The acidic pH of the chyme entering the duodenum stimulates the release of secretin, which increases the secretion of water and bicarbonate ions from the pancreas (Fieker & al., 2011 as cited in

Fig. 2. Schematic representation of the relative contributions of HGL and HPL to the overall digestion of dietary triacylglycerides. On a weight basis, the ratio of pancreatic lipase to gastric lipase total secretory outputs was found to be around four after 3 hours of digestion. The level of gastric hydrolysis was calculated to be 10% of the acyl chains released from the meal triglycerides. Gastric lipase remained active in the duodenum where it might still hydrolyze 7.5% of the triglyceride acyl chains. Hence, globally, during the whole digestion period, gastric lipase hydrolyzes 17.5% of all the triglyceride acyl chains. (Reproduced from

(BSSL)) will hydrolyze triglycerides, diglycerides, phospholipids, and esters of lipid-soluble vitamins and of cholesterol (Hui & Howles, 2002). Phospholipase A2 hydrolyzes phospholipids to lysophospholipids20 which is essential for an optimal absorption of lipid

Products generated during lipolysis are solubilized in bile salts–mixed micelles and liposomes (vesicles) which allow absorption across the intestinal villi. Once absorbed, the digested lipids are converted back to triglycerides, phospholipids, and esters of cholesterol and of lipid-soluble vitamins, then packaged as chylomicrons and transported through the thoracic duct into the systemic circulation for delivery to various sites throughout the body

To execute this digestive function, postprandial pancreatic juice secretion can increase up to 1 to 2 L per day in response to physiologic stimuli, mainly secretin and vagal output (Lee & Muallem, 2009). Appropriate enzyme delivery in the duodenum is allowed through a specific orchestration of the pancreatic fluid secretion during the fed state. In fact, during the gastric phase, digestion of proteins by pepsin and of triglycerides by gastric lipase generates amino acids and free fatty acids, respectively (Fieker & al., 2011, as cited in Alpers, 1994). When delivered through the pylorus, they become powerful stimulants of the cholecystokinin hormone (CCK) produced by the duodenal endocrine cells which stimulates pancreatic enzymes secretion and controls the gastric emptying rate. The acidic pH of the chyme entering the duodenum stimulates the release of secretin, which increases the secretion of water and bicarbonate ions from the pancreas (Fieker & al., 2011 as cited in

Carrière & al., 1993b).

nutrients (Fieker & al., 2011, as cited in Tso, 1994).

(Fieker & al., 2011, as cited in Tso, 1994).

Solomon, 1994). This gastric phase of digestion represents an important aspect in the overall postprandial regulation of pancreatic secretion. During the intestinal phase, enterohormones, such as CCK, together with neurotransmitters and neuropeptides further stimulate pancreatic secretion (Chey & Chang, 2001). Thus, digestive pancreatic enzyme response to a meal follows a specific pattern in which the degree and duration depend on nutrient composition, caloric content and physical properties of the meal. Enzyme secretion into the duodenum increases quickly reaching peak output within the first 20 to 60 minutes postprandially, then decreasing to a stable level before reaching an interdigestive level at the end of the digestive period, ie, about 4 hours after meal intake (Keller & Layer, 2005).


**7. Respiratory function exploration**

#### **7.1. Children under 2 years of age**

could have a strong prognostic value. However, Pohunek et al. [23] found no differences in ECP levels in children under 3, between both diagnoses when children were asymptomatic, as opposite to when they were suffering a crisis. From his work, it can be deducted the inter‐ est to assess the enzyme during a bronchobstructive crisis, in yet not diagnosed children, es‐ pecially during the first episode, for the possibility of establishing prophylactic measures to

**+1 SD +2 SD**

prevent or delay the establishment of asthma.

84 Asthma - From Childhood Asthma to ACOS Phenotypes

**Age Geometric mean**

**Table 2.** Normal serum IgE levels (Kjellman and Johanson, 1976).

**Table 3.** Non-allergic process more frequents in small children that occur with high IgE.

**Parasitic infections** *Ascaris lumbricoides Toxocara canis*

*Entamoeba haemolitica*

**Immunodeficiency disorders**

Wiskott-Aldrich S. Di George S. Hiper IgE S.

Selective IgA deficiency

*Echinococcus Trichinella spiralis*

*Filaria* Others **kU/l**

Umbilical cord 0.3 – – 6 weeks 0.7 2.1 6.1 3 months 0.8 1.8 3.8 6 months 2.7 6.6 16.3 9 months 2.4 4.2 7.3 12 months 7 21 58 2 years 11 26 61 3 years 11 21 40 4 years 20 37 70 7 years 26 75 221

In the diagnosis of asthma or of wheezy bronchitis, exploration in the infant has a relative utility. However, the greatest value of early exploration is focussed on distinguishing the processes that occur with breathing difficulties of various kinds, some of bronchopulmonary origin (cystic fibrosis, bronchopulmonary dysplasia, primary ciliary dyskinesia, bronchitis obliterans, malformations) or extrapulmonary (vascular rings, ductus persistence, other heart disease), which can raise the differential diagnosis with severe asthma or resistant to habitual treatment. Exploration in infants should be restricted due to the risk involved in the need to sedate the child, requiring hospital environment, which should be restricted to the following indications, in order to diagnose other possible diseases with apparent symptoms of asthma, although symptoms can have a different origin:

#### *Methodology*

The most common method is the rapid thoracoabdominal compression at ordinary volume. As the child breathes normally and at the end of an inspiration, an insufflation of the jacket is provoked to induce maximal forced expiration, thus obtaining the parameter of the maximum flow at functional residual capacity (VmaxFRC). Both the figure obtained and the appreciation of the layout of the flow-volume curve will provide information on the permeability of the airways and the degree of obstruction, if any.

Less suitable is the one based on thoracoabdominal compression provided by a pneumatic jacket, a kind of inflatable vest connected to an air compressor through a non-distensible thick tube. The exhaled airflow is measured with a pneumotachograph of appropriate size that adapts to the mouth through a mask. The biggest drawback is the need to sedate the child with chloral hydrate orally, which is not without risks.

As forced expiration is provoked during a normal respiratory movement, that is ordinary volume, this technique does not provide the value of the forced vital capacity (FVC) obtained with a spirometry, and therefore, no FEV1 or the FEV1/FVC ratio and FEV1% can be obtained. To acquire these values, we must perform the technique known as rapid thoracoabdominal compression with previous insufflation, which is artificially forcing a deep breath, for which, by a compressor connected to an oral–nasal mask, air is blown into child up to the maximum vital capacity and requiring a pressure of 2–3 kPa (20–30 cm H2O). Afterwards, a rapid inflation of the jacket is performed to provoke the forced expiration. This way, valuable data comparable to those provided by spirometry, can be obtained.

#### **7.2. Children over 2 years of age**

Although the following techniques are used in older children who do not cooperate during the exploration, some of them are also used in infants with devices adapted to their size (plethysmograph), requiring sedation of the child. With them, precise information on airway resistance (AWR) and compliance can be obtained.

The AWR is defined by the difference of pressure between both ends of the airways, that is the mouth and alveoli when an air flow of 1 l/s occurs. The circumstantial narrowing of the bronchi increases resistance, deducing the intensity of the obstruction by the degree of the increase in the value of the AWR.

Compliance refers to the intensity of the rigidity of the respiratory system, defined by the increase of the volume produced divided by the increase of the pressure unit, so that the less pressure necessary to produce an equal increase in volume, the higher the compliance.

The resistance can be measured through well-known techniques, such as interruption of flow (Rint), forced oscillation and its oscillometric impulse variation and plethysmography, a technique which also allows the compliance to be known.

#### *Flow interruption (Rint)*

The interruption of the airflow during normal breathing causes rapid and complete occlusion of the airways, enabling the measurement of the pressure in the oral cavity immediately before the interruption and during the normal respiratory cycle using a pneumotachograph. The measurement of the alveolar pressure is deduced from the pressure value established in the mouth when the momentary interruption of flow occurs. If this is suddenly interrupted, for a split second, an immediate rise in pressure occurs in the mouth. The pressure measured this way is very similar to that found in the alveoli, allowing the measurement of *resistance*, comparing this pressure with that prevailing in the mouth just before shutting off the flow. The Unit used to measure the resistance is Pascal in litres per second. In short, Rint is the most simple and affordable method to learn the AWR in young children, with the only requirement being that they breathe normally through the tube that is fitted into the mouth, preventing nasal breathing by pinching the nose.

#### *Forced oscillation: impulse oscillometry*

*Forced oscillometry* is based on the application of oscillatory pressure changes and therefore airflow, measuring the resistance from the relationship between the two. Easy to perform, it only requires that the child breathe calmly through a tube—not longer than 1 m—attached to the mouth and a volume of 100 ml, having inserted a pneumotachograph in between. The patient's air flow is superimposed with a oscillanting flow of 2 ml at a frequency of 10 Hz coming from a sinusoidal generator, thereby leading to pressure variations which are not perceived by the child and are proportional to the 'total' patient breathing resistance.

Best results are obtained with a newer variation of this process, the *impulse oscillometry* (IOS). A controlled deviation of the membrane of a loudspeaker, which is adapted to a nozzle, leads to the excitation of the airflow generating pressure impulses, from which ratio, the value of the central airways resistance and the lung elasticity is obtained; and therefore, the values result from the relationship between the exerted pressure and the airflow [4].

#### *Plethysmography*

tube. The exhaled airflow is measured with a pneumotachograph of appropriate size that adapts to the mouth through a mask. The biggest drawback is the need to sedate the child with

As forced expiration is provoked during a normal respiratory movement, that is ordinary volume, this technique does not provide the value of the forced vital capacity (FVC) obtained with a spirometry, and therefore, no FEV1 or the FEV1/FVC ratio and FEV1% can be obtained. To acquire these values, we must perform the technique known as rapid thoracoabdominal compression with previous insufflation, which is artificially forcing a deep breath, for which, by a compressor connected to an oral–nasal mask, air is blown into child up to the maximum vital capacity and requiring a pressure of 2–3 kPa (20–30 cm H2O). Afterwards, a rapid inflation of the jacket is performed to provoke the forced expiration. This way, valuable data comparable

Although the following techniques are used in older children who do not cooperate during the exploration, some of them are also used in infants with devices adapted to their size (plethysmograph), requiring sedation of the child. With them, precise information on airway

The AWR is defined by the difference of pressure between both ends of the airways, that is the mouth and alveoli when an air flow of 1 l/s occurs. The circumstantial narrowing of the bronchi increases resistance, deducing the intensity of the obstruction by the degree of the increase in

Compliance refers to the intensity of the rigidity of the respiratory system, defined by the increase of the volume produced divided by the increase of the pressure unit, so that the less pressure necessary to produce an equal increase in volume, the higher the compliance.

The resistance can be measured through well-known techniques, such as interruption of flow (Rint), forced oscillation and its oscillometric impulse variation and plethysmography, a

The interruption of the airflow during normal breathing causes rapid and complete occlusion of the airways, enabling the measurement of the pressure in the oral cavity immediately before the interruption and during the normal respiratory cycle using a pneumotachograph. The measurement of the alveolar pressure is deduced from the pressure value established in the mouth when the momentary interruption of flow occurs. If this is suddenly interrupted, for a split second, an immediate rise in pressure occurs in the mouth. The pressure measured this way is very similar to that found in the alveoli, allowing the measurement of *resistance*, comparing this pressure with that prevailing in the mouth just before shutting off the flow. The Unit used to measure the resistance is Pascal in litres per second. In short, Rint is the most simple and affordable method to learn the AWR in young children, with the only requirement

chloral hydrate orally, which is not without risks.

86 Asthma - From Childhood Asthma to ACOS Phenotypes

to those provided by spirometry, can be obtained.

resistance (AWR) and compliance can be obtained.

technique which also allows the compliance to be known.

**7.2. Children over 2 years of age**

the value of the AWR.

*Flow interruption (Rint)*

A plethysmograph measures the changes in volume of the thorax. Its principle is the law of Boyle and Mariotte, whereby the volume occupied by a mass of gas, at constant temperature, is inversely proportional to the pressure. By plethysmography, intrathoracic gas volume (TGV) through the volumetric variations of the thorax is measured simultaneously with the AWR, and from these values, conductance can be calculated.

#### *Bronchodynamic tests*

The above techniques report on the current state of the permeability of the lower airways but do not provide information on the level of BHR, the increase of which is significant in the diagnosis of asthma. Hence, the need to carry out tests to make it evident, that is bronchocon‐ strictor (methacholine, histamine) and bronchodilator (β-mimetic) tests. The three technical variations mentioned can be used for this purpose


*2.1. Bistatic Radar Cross Section of the Ocean Surface*

To derive the bistatic radar cross section of the ocean surface, we follow the method of Barrick [12], where the equivalent monostatic radar cross section was derived. In his work, Barrick used the perturbation analysis of Rice [14] where, by assuming small waveheights and slopes, the electric field scattered from the ocean surface, *Es*, was calculated. They key points of the derivation follow, however, more details can be found in the work of Hardman [25].

The value of *Es* depends on both the incident radio waves and the properties of the scattering surface. Firstly, the incident waves will propagate as vertically polarised ground waves. Secondly, as the ocean varies in both time and space, by assuming that these variations are periodic and that the surface is of infinite extent, we can define the surface, *f*(*x*, *y*, *t*), as a Fourier series expansion, such that

$$z = f(x, y, t) = \sum\_{mnl = -\infty}^{\infty} P(m, n, l) \mathbf{e}^{ia(mx + ny) - i nlt},\tag{4}$$

for wavenumber *a* = 2*π*/*L*, angular frequency *w* = 2*π*/*T* and Fourier coefficients *P*(*m*, *n*, *l*) which are dependent on the integers *m*, *n* and *l*.

*Remote Sens.* **2020**, *12*, 313

The electric field scattered from this surface, will also be periodic with the same fundamental spatial and temporal periods and hence Rice defined - *Es* as a Fourier series. For a perfectly conducting flat surface, the exact solution can be found. Therefore, we perturb the solution around the flat surface, with ordering parameter *k*0 *f* (for radar wavenumber *k*0), using Maxwell's equations and the tangential boundary condition to obtain the first and second order Fourier coefficients. Details of the calculations for vertically polarised waves can be found in the work of Hardman [25]; for horizontally polarised waves, the details are provided by Rice [14]. The resulting scattered electric field has components

$$\begin{split} E\_x &= 2\sum\_{mml} E(m, n, z, l) e^{-i\omega\_0 t} \left[ i(k\_0 - am)P(m - \nu, n, l) \right] \\ &+ \sum\_{qrs} \left\{ a^2 (m - q)(\nu - q) k\_0 + (k\_0 - am)b^2(q, r) \right\} Q(m, n, l, q, r, s) \right], \\ E\_y &= 2a \sum\_{mml} E(m, n, z, l) e^{-i\omega\_0 t} \left[ -inP(m - \nu, n, l) \right. \tag{6} \\ &+ \sum\_{qrs} \left\{ a(n - r)(\nu - q) k\_0 - nb^2(q, r) \right\} Q(m, n, l, q, r, s) \Bigg] \\ E\_z &= 2a^2 \theta^{\mathrm{an}} e^{-i\omega\_0 t} + 2 \sum\_{mml} \frac{E(m, n, z, l)}{b(m, n, l)} e^{-i\omega\_0 t} \left[ \left( -i(a(m - \nu) k\_0 + b^2(m, n)) \right) P(m - \nu, n, l) \right. \\ &\left. + \sum\_{qrs} \left\{ \left( a^3 (q - \nu) (m^2 + n^2 - qm - rn) k\_0 \right) \right. \right. \tag{7} \\ &\left. + \left. a(a(m^2 + n^2) - mk\_0) b^2(q, r) \right] Q(m, n, l, q, r, s) \right], \end{split} \tag{7}$$

where *ω*0 is the angular frequency of the emitted radio waves,

$$E(m, n, z, l) = \mathbf{e}^{i(a(mx+ny) + b(m,n)z)} \mathbf{e}^{-iwlt}$$

in which

$$b(m,n) = \begin{cases} (k\_0^2 - a^2m^2 - a^2n^2)^{1/2} & \text{if } m^2 + n^2 < k\_0^2/a^2\\\ i(a^2m^2 + a^2n^2 - k\_0^2)^{1/2} & \text{if } m^2 + n^2 > k\_0^2/a^2 \end{cases},$$

and

$$Q(m,n,l,q,r,s) = \frac{P(q-\nu,r,s)P(m-q,n-r,l-s)}{b(q,r)}.$$

By definition, the electric field in Equations (5)–(7) corresponds to the scattering of infinite plane waves from a surface of infinite extent. To transform the fields to finitely scattered fields, which is necessary as only a portion of the whole ocean will be illuminated by the radar, we can use the equation presented by Johnstone [21] who followed the work of Stratton [26]. He showed that if the electric field is known on a finite section of an infinitely large volume such as the surface *S*1 on the hemisphere shown in Figure 4, then the scattered electric field at a point (*x* , *y* , *z* ) inside of the volume can be calculated.

The equation is given by

$$\begin{split} \mathcal{E}(x', y', z') &= \frac{\mathbf{e}^{ik\_0 R}}{4\pi R} \int\_{S\_1} \left[ \left( \left( \frac{\partial E\_x}{\partial z} - \frac{\partial E\_z}{\partial x} \right) \vec{d}\_x + \left( \frac{\partial E\_y}{\partial z} - \frac{\partial E\_z}{\partial y} \right) \vec{d}\_y \right)\_{z=0} \right. \\ &\left. + ik\_0 \left[ E\_x \cos\theta \vec{d}\_x + E\_y \cos\theta \vec{d}\_y - \left( E\_x \sin\theta \cos\varphi + E\_y \sin\theta \sin\varphi \right) \vec{d}\_z \right]\_{z=0} \\ &\quad + \left[ \left( \frac{\partial E\_z}{\partial x} - \frac{\partial E\_x}{\partial z} \right) \sin\theta \cos\varphi + \left( \frac{\partial E\_z}{\partial y} - \frac{\partial E\_y}{\partial z} \right) \sin\theta \sin\varphi \right]\_{z=0} \\ &\quad \cdot \left[ \sin\theta \cos\varphi \vec{d}\_x + \sin\theta \sin\varphi \vec{d}\_y + \cos\theta \vec{d}\_z \right] \right] \mathbf{e}^{-i\vec{k}\_0 \cdot \rho} dS\_{1,z} \end{split} \tag{8}$$

where *ρ* is the vector (*x*, *y*, *z*) on *S*1, (*R*, *θ*, *ϕ*) are the radius, polar angle and azimuthal angle measured from the origin to (*x* , *y* , *z* ) and *k* -0 is the radar wavevector given by

**Figure 4.** The finite scattering surface, *S*1, with boundary *C*, as part of a hemispherical surface. The vector *ρ* denotes the position (*x*, *y*, *z*) on *S*1; the vector*rr* is the vector from (*x*, *y*, *z*) to some distant point (*x* , *y* , *z* ) where the scattered electric field is desired. The vector *k* -0 is the radar wavevector in the direction of the scattered radio wave, - *R*.

Note that the integral can be evaluated on any plane and *z* = 0 is used for convenience. However, as pointed out by Hisaki and Tokuda [24], this choice is in fact the infinite scattering surface limit. Evaluating the integral on *z* = *f* as they did changes the resulting power spectrum of the scatter but differences are very small at the Doppler frequencies used for inversion so *z* = 0 is sufficient for this work. To find the scattered field at a point (*x* , *y* , *z* ), the values for *Ex*, *Ey* and *Ez* from Equations (5)–(7) are substituted into Equation (8) and the integral is calculated. The vertically polarised component, *Eθ* (*t*), is then identified in the resulting expression (as these are the radio waves that the receiver will detect) such that

$$\begin{split} E\_{\theta}(t) &= \frac{i e^{i\mathbf{k}\_{0} \cdot \mathbf{R}}}{2\pi R} L^{2} \sum\_{nml} \left\{ B(t) \left[ -i\mathbf{x}\_{1} P(m-\nu,n,l) + \sum\_{qrs} x\_{2} Q \right] + \mathcal{C}(t) \left[ -i\mathbf{y}\_{1} P(m-\nu,n,l) + \sum\_{qrs} y\_{2} Q \right] \\ &+ D(t) \left[ -i\mathbf{z}\_{1} P(m-\nu,n,l) + \sum\_{qrs} z\_{2} Q \right] \right\}, \end{split} \tag{9}$$

where,

$$\begin{aligned} x\_1 &= am - k\_0; & x\_2 &= a^2(m - q)(\nu - q)k\_0 + (k\_0 - am)b^2(q, r) \\ y\_1 &= an; & y\_2 &= a^2(n - r)(\nu - q)k\_0 - anb^2(q, r) \\ z\_1 &= a(m - \nu)k\_0 + b^2(m, n); & z\_2 &= \left[a^3(q - \nu)(m^2 + n^2 - qm - rn)k\_0 + a\left(a(m^2 + n^2) - mk\_0\right)b^2(q, r)\right]. \end{aligned}$$

and,

$$B(t) = \sum\_{mnl} \cos \varphi (k\_0 + b(m, n) \cos \theta) \sin(XR) \sin(YR) e^{-i(wl + \omega\_0)t} \tag{10}$$

$$\mathbf{C}(t) = \sum\_{mnl} \sin \varrho (k\_0 + b(m, n) \cos \theta) \sin \mathbf{c}(XR) \sin \mathbf{c}(YR) \mathbf{e}^{-i(wl + \omega y)t} \tag{11}$$

$$D(t) = \sum\_{mnl} -\cos\theta (am\cos\varphi + an\sin\varphi) \frac{\text{sinc}(XR)\,\text{sinc}(YR)}{b(m,n)} \mathbf{e}^{-i(wl+\omega\_0)t},\tag{12}$$

for *XR* = *L* 2 (*am* − *k*0 sin *θ* cos *ϕ*) and *YR* = *L* 2 (*an* − *k*0 sin *θ* sin *ϕ*).

In the scattered electric field in Equation (9), the first order components (namely, the terms including a single *P* term) represent the single scattering of one electromagnetic wave, to the receiver, from one ocean wave. The second order components (which include a factor of *Q*) represent doubly scattered electromagnetic waves, to the receiver, from two single ocean waves. The order of the ocean wave, currently denoted by *P*(*m* − *ν*, *n*, *l*), has not yet been considered and is assumed to be first order. However, in making such an assumption, a second order contribution from first order scattering from second order oceans waves is missed, where a second order ocean wave is the result of the nonlinear interaction between two first order ocean waves.

To allow for the second order hydrodynamic effects in shallow water, Barrick and Lipa [27] used a perturbation method to relate the second order coefficients *P*(2)( *k*, *ω*), of a surface defined by *z* = ∑*k*,*ω P*( *k*, *ω*)e*i k*·*r*−*iωt* , to the first order coefficients *P*(1)( *k*, *ω*). Their method involved expanding the surface height Fourier coefficients around the flat surface, i.e.,

$$P(\vec{k},\omega) = P^{(1)}(\vec{k},\omega) + P^{(2)}(\vec{k},\omega) + \dots,$$

alongside boundary conditions from the equations of motion, also expanded to second order. They showed that for ocean waves with wavevectors *k* -1 and *k* -2, with corresponding angular frequencies *ω*1 and *ω*2 (related by the dispersion relation of ocean waves given by *ω* = *gk* tanh(*kd*)),

$$P^{(2)}(\vec{k}^{\prime\prime},\omega^{\prime\prime}) = \sum\_{\vec{k\_1}\vec{k\_2}} \sum\_{\omega\gamma\cup\omega\_2} \Gamma\_H(\vec{k\_1},\omega\_1,\vec{k\_2},\omega\_2) P^{(1)}(\vec{k\_1},\omega\_1) P^{(1)}(\vec{k\_2},\omega\_2),\tag{13}$$

where *k* - = *k* -1 + *k* -2, *ω* = *ω*1 + *ω*2, and

$$\begin{split} \Gamma\_{H} &= \frac{1}{2} \left\{ k\_{1} \tanh(k\_{1}d) + k\_{2} \tanh(k\_{2}d) + \frac{\omega \prime \prime}{g} \frac{(\omega\_{1}^{3} \operatorname{csch}^{2}(k\_{1}d) + \omega\_{2}^{3} \operatorname{csch}^{2}(k\_{2}d))}{(\omega \prime \prime - gk \prime \tanh(k^{\prime}d))} \right. \\ &\left. + \frac{(k\_{1}k\_{2} \tanh(k\_{1}d) \tanh(k\_{2}d) - \vec{k}\_{1} \cdot \vec{k}\_{2})}{\sqrt{k\_{1}k\_{2} \tanh(k\_{1}d) \tanh(k\_{2}d)}} \left( \frac{g k^{\prime\prime} \tanh(k^{\prime}d) + \omega^{\prime\prime 2}}{g k^{\prime\prime} \tanh(k^{\prime}d) - \omega^{\prime\prime 2}} \right) \right\}, \end{split} \tag{14}$$

is called the *hydrodynamic coupling coefficient*.

To include the second order hydrodynamic effects in the scattered electric field, we expand *P*(*m* − *ν*, *n*, *l*) into *P*(1)(*m* − *ν*, *n*, *l*) + *P*(2)(*m* − *ν*, *n*, *l*) and then substitute in the value of *P*(2)(*m* − *ν*, *n*, *l*) using Equation (13) (by letting *k* -= (*m* − *ν*, *n*) and *ω* = *l*), and so Equation (9) becomes

$$E\_{\theta}(t) = \frac{i e^{ik\_{0}R}}{2\pi R} L^{2} \sum\_{mml} \left\{ -i l\_{\text{s}}^{\prime\prime}(t) P^{(1)}(m - \nu, n, l) + \sum\_{qrs} [-i l\_{\text{s}}^{\prime\prime}(t) \Gamma\_{l} b(p, q) + \overline{\xi}(t)] \right. \\ \left. Q(m, n, l, q, r, s) \right\}, \tag{15}$$

where for brevity

$$\mathcal{Z}(t) = B(t)\mathbf{x}\_1 + \mathcal{C}(t)y\_1 + D(t)z\_1$$

*Remote Sens.* **2020**, *12*, 313

and

$$\mathcal{G}(t) = B(t)\mathbf{x}\_2 + \mathcal{C}(t)\mathbf{y}\_2 + D(t)z\_2.$$

Following Johnstone [21], we finally calculate the radar cross section by substituting Equation (15) into

$$\sigma(\omega) = \lim\_{R \to \infty} 4\pi R^2 \frac{\mathcal{F}\left[ \langle E\_{\theta}(t\_1) E\_{\theta}^\*(t\_2) \rangle \right]}{L^2},\tag{16}$$

where *R* is the distance from the scatter patch to the receiver and F denotes a Fourier transform, with definition

$$\mathcal{F}[f(t)] = \frac{1}{2\pi} \int\_{\infty}^{\infty} f(t)e^{-i\omega t} \, dt. \tag{17}$$

To calculate Equation (16), the following properties of the surface height Fourier coefficients are used:

• The Fourier coefficients are normally distributed about zero; hence

$$
\langle P(m, n, l) \rangle = 0.\tag{18}
$$

• As the surface is real, *f*(*x*, *y*, *t*) is equal to *f* ∗(*x*, *y*, *t*), which is true when

$$P(-m, -n, -l) = P^\*(m, n, l). \tag{19}$$

• From Thomas [28],

$$
\langle P\_1 P\_2 P\_3 \rangle = 0 \tag{20}
$$

and

$$
\langle P\_1 P\_2 P\_3 P\_4 \rangle = \langle P\_1 P\_2 \rangle \langle P\_3 P\_4 \rangle + \langle P\_1 P\_3 \rangle \langle P\_2 P\_4 \rangle + \langle P\_1 P\_4 \rangle \langle P\_2 P\_3 \rangle. \tag{21}
$$

• The surface roughness spectrum *S*(*p*, *q*, *wl*), found by utilising the Wiener–Khinchin theorem, is related to the surface height Fourier coefficients by

$$P(P(m,n,l)P(q,r,s)) = \begin{cases} \frac{(2\pi)^3 S(p\_\prime q\_\prime, wl)}{L^2 T} & \text{if } q\_\prime r\_\prime s = -m\_\prime - n\_\prime - l\\ 0 & \text{if else} \end{cases} \tag{22}$$

where *p* = *am* and *q* = *an*.

Then, substituting *Eθ* (*t*) from Equation (15) into Equation (16) and using Equation (20) leads to

$$\begin{split} \sigma(\omega) &= \frac{1}{\pi} \mathcal{F} \left[ \mathbf{L}^{2} \sum\_{\begin{subarray}{c} \text{null} \\ \mathbf{m}' \mathbf{n}' \end{subarray}} \left\{ \mathbb{J}(t\_{1}) \mathbb{J}^{\prime \*}\_{\mathbf{s}}(t\_{2}) \left\langle P^{(1)}(m-\nu,n,l) P^{(1)^{\prime}\*}(m'-\nu,n',l') \right\rangle \right. \\\\ &+ \sum\_{\begin{subarray}{c} \text{\$q\$rr\$} \\ \mathbf{q}' \mathbf{r} \text{s}' \end{subarray}} \left\{ \left[ -\mathbf{i}\_{\mathbf{s}}^{\prime}(t\_{1}) b(\mathbf{q},r) \Gamma\_{\mathrm{H}} + \mathbf{j}\_{\mathbf{s}}^{\prime}(t\_{1}) \left[ \left[ \mathbf{i}\_{\mathbf{s}}^{\prime \prime \*}(t\_{2}) b^{\ast}(\mathbf{q}^{\prime},r^{\prime}) \Gamma\_{\mathrm{H}}^{\prime} + \mathbf{j}\_{\mathbf{s}}^{\prime \*}(t\_{2}) \right] \left\langle Q Q^{\prime \*} \right\rangle \right] \right\} \right], \end{split} \tag{23}$$

where the arguments of *Q* are implied. The calculation of Equation (23) can be separated into its first and second order terms, such that

$$
\sigma(\omega) = \sigma^{(1)}(\omega) + \sigma^{(2)}(\omega),
$$

where the first order radar cross section, *σ*(1)(*ω*), is defined by the term including the average ) *P*(1)(*m* − *ν*, *n*, *l*)*P*(1) ∗(*m* − *ν*, *n* , *l* ) \* , and the second order, *σ*(2)(*ω*), including *QQ*∗. To calculate each of *σ*(1)(*ω*) and *σ*(2)(*ω*), the properties in Equations (18)–(22) are used to enforce restrictions on the Fourier coefficients and to introduce the roughness spectrum *S*( *k*). The mathematical details are spared here, but can be found in the work of Hardman [25].